phd process optimization

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Optimization and Operational Research PhD

Awards: PhD

Study modes: Full-time, Part-time

Funding opportunities

Programme website: Optimization and Operational Research

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Research profile

The work in the Operational Research and Optimization research group is in three main areas: the mathematical and computing aspects of optimization, combinatorial optimization, and energy systems.

The core technology in optimization is the solution of large sparse linear and quadratic problems, and we provide world-class expertise in the two main solution methods for these: the simplex method and the interior point method. In combinatorial optimization, we provide expertise for modelling real-world problems using integer linear programming formulations and for deriving efficient exact and heuristic algorithms to solve them.

Specialist expertise in energy includes optimization of system planning and optimization, security of supply risk analysis, and decision support for public policy. We also have interests in PDE-constrained optimization, global optimization, decomposition methods, parallel computing, industrial applications of optimization and stochastic optimization.

Specific topics which could yield PhD projects include:

• Algorithms for linear and nonlinear nonconvex smooth optimization problems
• Optimization methods for linear, integer linear, quadratic and nonlinear programming
• Decomposition methods for large-scale nonlinear nonconvex constrained optimization
• Bundle methods
• Warm starts for interior point methods
• Pooling problems
• Applications of optimization in logistics
• Parameter uncertainty in queueing theory and revenue management.
• Facility location and vehicle routing

Training and support

Being part of the Operational Research and Optimization group will give you the opportunity to meet and confer with academics worldwide. You will be a member of the Edinburgh Research Group in Optimization (ERGO) which, through its regular seminar series, attracts local and international researchers interested in the development of operational research and optimization. As a group, we are currently collaborating with researchers in Denmark, the Netherlands, Canada, USA, Italy, Norway, China, France, Spain, Germany and Turkey, and are invited to give addresses and organise workshops at major optimization, OR and energy conferences.

You will enjoy excellent facilities, ranging from one of the world’s major supercomputing hubs to libraries for research at the leading level, including the new Noreen and Kenneth Murray Library at King’s Buildings.

Students have access to more than 1,400 computers in suites distributed across our University’s sites, many of which are open 24 hours a day. In addition, if you are a research student, you will have access to dedicated desk space with monitors and a laptop computer.

We provide all our mathematics postgraduates with access to software packages such as:

• Mathematica

Research students are allocated parallel computing time on ‘Eddie’, the Edinburgh Compute and Data Facility. You can also request use of the BlueGene/Q supercomputer facility for your research.

VIDEO: Operational Research (OR) MSc Graduates

Entry requirements.

These entry requirements are for the 2024/25 academic year and requirements for future academic years may differ. Entry requirements for the 2025/26 academic year will be published on 1 Oct 2024.

A UK first class honours degree, or its international equivalent, in an appropriate subject; or a UK 2:1 honours degree plus a UK masters degree, or their international equivalents; or relevant qualifications and experience.

International qualifications

Check whether your international qualifications meet our general entry requirements:

• Entry requirements by country
• English language requirements

Regardless of your nationality or country of residence, you must demonstrate a level of English language competency at a level that will enable you to succeed in your studies.

English language tests

We accept the following English language qualifications at the grades specified:

• IELTS Academic: total 6.5 with at least 6.0 in each component. We do not accept IELTS One Skill Retake to meet our English language requirements.
• TOEFL-iBT (including Home Edition): total 92 with at least 20 in each component. We do not accept TOEFL MyBest Score to meet our English language requirements.
• C1 Advanced ( CAE ) / C2 Proficiency ( CPE ): total 176 with at least 169 in each component.
• Trinity ISE : ISE II with distinctions in all four components.
• PTE Academic: total 62 with at least 59 in each component.

Your English language qualification must be no more than three and a half years old from the start date of the programme you are applying to study, unless you are using IELTS , TOEFL, Trinity ISE or PTE , in which case it must be no more than two years old.

Degrees taught and assessed in English

We also accept an undergraduate or postgraduate degree that has been taught and assessed in English in a majority English speaking country, as defined by UK Visas and Immigration:

• UKVI list of majority English speaking countries

We also accept a degree that has been taught and assessed in English from a university on our list of approved universities in non-majority English speaking countries (non-MESC).

• Approved universities in non-MESC

If you are not a national of a majority English speaking country, then your degree must be no more than five years old* at the beginning of your programme of study. (*Revised 05 March 2024 to extend degree validity to five years.)

Find out more about our language requirements:

• Academic Technology Approval Scheme

If you are not an EU , EEA or Swiss national, you may need an Academic Technology Approval Scheme clearance certificate in order to study this programme.

Fees and costs

Tuition fees.

Scholarships and funding

Featured funding.

• School of Mathematics funding opportunities
• Research scholarships for international students

UK government postgraduate loans

If you live in the UK, you may be able to apply for a postgraduate loan from one of the UK's governments.

The type and amount of financial support you are eligible for will depend on:

• your programme
• the duration of your studies
• your tuition fee status

Programmes studied on a part-time intermittent basis are not eligible.

• UK government and other external funding

Other funding opportunities

Search for scholarships and funding opportunities:

• Search for funding

Further information

• Graduate School Administrator
• Phone: +44 (0)131 650 5085
• Contact: [email protected]
• School of Mathematics
• James Clerk Maxwell Building
• Peter Guthrie Tait Road
• The King's Buildings Campus
• Programme: Optimization and Operational Research
• School: Mathematics
• College: Science & Engineering

Select your programme and preferred start date to begin your application.

PhD Optimization and Operational Research - 3 Years (Full-time)

Phd optimization and operational research - 6 years (part-time), application deadlines.

We strongly recommend you submit your completed application as early as possible, particularly if you are also applying for funding or will require a visa. We may consider late applications if we have places available. All applications received by 22 January 2024 will receive full consideration for funding. Later applications will be considered until all positions are filled.

• How to apply

You must submit two references with your application.

Find out more about the general application process for postgraduate programmes:

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Operations Research and Optimization

Our faculty, whose expertise in operations research includes subfields in optimization, such as continuous, discrete, and stochastic optimization, conduct research with important applications in healthcare, astronomy, vision, network modeling, defense systems, and scheduling. This diversity in research foci, involving both theory and application areas, involves undergraduate and graduate students.

Faculty and students in operations research and optimization benefit from affiliations and collaborations across the university, including with JHU’s Applied Physics Laboratory, the Institute for Computational Medicine (ICM), the JHU Systems Institute, and the JHU Algorithms and Complexity Group. These affiliations and associated collaborations make our group a great example of the truly interdisciplinary nature that is characteristic of Johns Hopkins University.

Research Affiliations at Johns Hopkins University

• JHU Applied Physics Laboratory
• Institute for Computational Medicine
• Center for Systems Science and Engineering
• Machine Learning Group

Primary Areas of Research

Operations research.

Operations research aims to provide a framework to model complex decision-making problems that arise in engineering, business and analytics, and the mathematical sciences, and investigates methods for analyzing and solving them. The most common solution techniques include mathematical optimization, simulation, queuing theory, Markov decision processes, and data analysis, all of which use mathematical models to describe the system.

Optimization

Optimization focuses on finding the minimum (or maximum) value of an objective function subject to constraints that represent user preferences and/or limitations imposed by the nature of the question at hand. Research in optimization involves the analysis of such mathematical problems and the design of efficient algorithms for solving them. It is therefore no surprise that optimization, while integral to operations research, has become an indispensable tool in other areas such as statistics, machine learning, computer vision, and computational biology, just to name a few. Optimization technologies provide examples of how deep mathematical techniques help to provide concrete computational tools for solving a diverse suite of problems. Consequently, the knowledge and experience gained by students who study optimization will make them highly competitive in the job market.

Related Courses

Complete descriptions appear in the course catalog .

View the semester course schedule .

• EN.553.361    Intro to Optimization
• EN.553.362    Introduction to Optimization II
• EN.553.371    Cryptology and Coding
• EN.553.4/600    Mathematical Modeling and Consulting
• EN.553.4/653    Mathematical Game Theory
• EN.553.4/661    Optimization in Finance
• EN.553.4/663    Network Models in Operations Research
• EN.553.4/665    Introduction to Convexity
• EN.553.4/693    Mathematical Image Analysis
• EN.553.730    Statistical Theory
• EN.553.731    Statistical Theory II
• EN.553.761    Nonlinear Optimization I
• EN.553.762    Nonlinear Optimization II
• EN.553.764    Modeling, Simulation, and Monte Carlo
• EN.553.765    Convex Optimization
• EN.553.766    Combinatorial Optimization
• EN.553.792    Matrix Analysis and Linear Algebra
• EN.553.735    Topics in Statistical Pattern Recognition

Research and academic opportunities in operations research and optimization

PhD in Operations Research

WHAT IS OPERATIONS RESEARCH?

Operations research (OR) is the discipline of applying advanced analytical methods—such as optimization, statistics, machine learning, and probability—to make better decisions that impact society and the world positively.

The mission of the PhD program is intimately linked to the mission of the ORC.

Phone:  617-253-3601 Email:   [email protected]

MIT’s doctoral degree (PhD) program in operations research (OR) provides you with thorough understanding of the theory of OR while teaching you to how to develop and apply OR methods in practice.

We offer a general degree track as well as three optional degree tracks in operations management , networked systems , and analytics . All doctoral students must complete the general degree track requirements; those who choose an optional degree track will have additional, specialized requirements to fulfill. 

General Degree Track

In addition to the writing competency requirements, our rigorous curriculum includes challenging coursework, action learning, and innovative research.

You’ll take eight graduate-level classes that have been approved by the ORC co-directors, including at least two courses in optimization, at least three in applied probability and statistics, and at least one in OR modeling.

You’ll put OR theory into practice through valuable, hands-on learning experiences, completing one of the following:

• Option 1: Participate in a summer internship, during which you’ll create OR models that address a real-world problem.
• Option 2: Undertake a project with an ORC faculty member, either as part of a supervised research activity or as an extra part of a regular course offering.
• Option 3: Take part in a class, for which you’ll build and implement OR models that have practical applications.

And, you’ll conduct in-depth research on a topic that complements your academic interests and career goals. You’ll write a thesis based on the independent research you conduct under the guidance of our expert faculty.

Qualifying Process and General Examination

All students enrolled in an ORC doctoral program must complete the Qualifying Process and receive a passing score on the General Examination.

• Students must choose one approved course from the three different categories (Optimization, Probability, and Machine Learning/Statistics). 
• Students must satisfactorily complete the three courses and receive two As and 1 B by the end of their third semester at MIT.  Of the 2 As, only one of those can be an A-.
• In their first year, students are required to register and take for credit the software tools course (15.S60) offered during IAP (January) led by current ORC students.
• During the student’s first summer at MIT (month of August), doctoral students will engage in a Common Experience project where students will work in teams to address an important problem for an organization.   
• General Examination : Students are required to take the General Examination once they have passed the Qualifying Process.  The General Exam is comprised of a research-oriented (RO) paper and an oral presentation of the RO paper and a discussion on a research paper selected by the General Exam Committee.

Upon completion of our doctoral program, you’ll have the specialized knowledge and technical skills to have a positive impact in a variety of fields, including business, education, and research. Many of our graduates have gone on to careers in academia, in the U.S. and abroad, while others have found success in business and industry as researchers and consultants.

 Analytics Track

In addition to the general PhD degree requirements, you will also:

• complete a summer internship with an organization related to analytics for your hands-on learning experience.
• take two specialized courses in analytics; these classes may count toward your eight required graduate-level classes.
• serve as a teaching assistant in courses related to analytics, or an approved equivalent.
• write a thesis on a topic related to analytics; one member of your thesis committee should be among the ORC faculty who specialize in analytics.

Networked Systems Track

• complete a summer internship with an organization related to networked systems for your hands-on learning experience.
• take two specialized courses in networked systems; these classes may count toward your eight required graduate-level classes.
• serve as a teaching assistant in courses related to networked systems, or an approved equivalent.
• write a thesis on a topic related to networked systems; one member of your thesis committee should be among the ORC faculty who specialize in networked systems.

Operations Management Track

• complete a summer internship with an organization related to operations management for your hands-on learning experience.
• take two specialized courses in operations management; these classes may count toward your eight required graduate-level classes. 
• serve as a teaching assistant in two MBA courses related to operations management or assist in one and take another one for credit. At least one of the classes for which you’re a teaching assistant must include recitation.
• write a thesis on a topic related to operations management; one member of your thesis committee should be among the ORC faculty who specialize in operations management.

For more information about our PhD program, please see our General Exam Syllabus .

For more information about ORC course offerings, please go here .

PhD Research Specializations

Main navigation.

Learn more about research specializations below. Then, rank your top two research areas of interest (1 being the most interested) in your application.

Computational Social Science

Decision and risk analysis, operations research.

Organizations, Technology and Entrepreneurship

Policy and Strategy

Quantitative finance.

Characterized by its social science depth, state-of-the-art methods, and field-based understanding of technology firms and markets.

Focuses on: - Analysis and design of public policy - Crowdsourcing - Coordination in online labor markets - Casual inference and experimentation

Courses to Take Statistics, computer science, optimization, economics, sociology, and possibly other social sciences

Recent Dissertations Recent PhD dissertations include: - Design and analysis of a peer-to-peer credit network and reputation system - Analysis of dynamic online markets - Design and analysis of flash teams - Fast algorithms for large scale personalized recommendations

Program and Center Affiliations Social Algorithms Lab (SOAL) Center for Work, Technology & Organization (WTO)

Focuses on applying engineering systems analysis and probability to complex economic and technical design or management problems, in the private and public sectors.

The Engineering Risk Research Group (ERRG) focuses on: - complex engineered systems (e.g., optimal architecture of satellites and deflection of asteroids’ trajectories) - cyber security, and risks in games against adversaries (e.g., counter-terrorism, counter-insurgency, and staying ahead of narco-traffickers).

Courses to Take Courses include the mathematical foundations of modeling dynamic environments, value and management of uncertain opportunities and risks, and public policy and strategy applications. Risk analysis requires optimization, stochastic processes, economics and game theory courses.

Recent Dissertations Recent PhD dissertations include: - Experiment sample sizes for influence diagrams - Markov process regression - Quantile function methods for decision analysis

Focuses on developing and applying analytical, computational, and economic tools to address a wide variety of problems in business, government, and society. The area is characterized by its mathematical depth, broad applicability, and interdisciplinary nature and has a particular emphasis in developing and applying models and algorithms to gain new insights and make better decisions across multiple domains.

Courses to Take

PhD students take core courses in optimization and stochastics as well as advanced courses in computer science, game theory, microeconomics, statistics, and other areas tailored to the interests of the student, e.g. Computational Social Science, Operations Management, Environmental Policy, Health Policy, etc.

Program and Center Affiliations Institute for Computational and Mathematical Engineering (ICME)

Organization, Technology and Entrepreneurship

Characterized by the study of technical work, technology’s effects on individuals and teams, the formation and growth of entrepreneurial firms, and strategy and innovation in technology-based firms.

Courses to Take Organization theory, organizational behavior, sociology, social psychology, economics, entrepreneurship, and strategy, as well as methods courses in statistics, experimental methods, inductive case studies, computational tools field research methods courses including ethnography, and social network analysis.

Recent Dissertations Recent PhD dissertations include: - Collaborations of private and public sector organizations to create breakthrough technologies - Collective innovation - Competitive interaction in the software industry - Educational reforms and their implications for entrepreneurship in China - Flash teams - Global collaboration - Occupational identities - Platform competition - Regulatory reforms and innovation in medical device industry - Social movements

Program and Center Affiliations Center for Work, Technology, and Organizations (WTO) Stanford Technology Ventures Program (STVP)

Focuses on the design and analysis of public policies and corporate strategies, especially those with technology-based issues.  Sub-areas include Energy and Environment, Health Systems Modeling and Policy, and National Security Policy.

Courses to Take It features a grounding in microeconomics and modeling approaches. Students take courses with a policy focus include such topics such as national security, energy and environment, and health care, and courses with a strategy focus cover topics such as entrepreneurship, innovation, and product development.

Recent Dissertations Recent PhD dissertations include: -Managing uncertainty in medical decision making -Resource allocation for infectious disease control -Optimizing patient treatment decisions in the presence of rapid technological advances -Economic analysis of HIV prevention and treatment portfolios.

Program and Center Affiliations Center for Health Policy/Program on Clinical Outcomes Research (CHP/PCOR) in the Medical School Energy Modeling Forum Precourt Energy Efficiency Center Systems Utilization Research for Stanford Medicine

Focuses on the quantitative and statistical study of financial risks, institutions, markets, and technology.

Courses to Take Students take courses in probability, statistics, optimization, finance, economics, computational mathematics, and computer science as well as a variety of other courses.

Recent Dissertations Recent PhD dissertations include: - Studies of machine learning methods for risk management - Systemic financial risk - Algorithmic trading - Optimal order execution - Large-scale portfolio optimization - Mortgage markets -Statistical testing of financial models

Program and Center Affiliations Advanced Financial Technologies Laboratory (AFTLab)

We have 118 optimization PhD Projects, Programmes & Scholarships

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optimization PhD Projects, Programmes & Scholarships

Evolutionary optimization, phd research project.

PhD Research Projects are advertised opportunities to examine a pre-defined topic or answer a stated research question. Some projects may also provide scope for you to propose your own ideas and approaches.

Funded PhD Project (Students Worldwide)

This project has funding attached, subject to eligibility criteria. Applications for the project are welcome from all suitably qualified candidates, but its funding may be restricted to a limited set of nationalities. You should check the project and department details for more information.

Efficient and Reliable Numerical Solution of Dynamic Optimization

Self-funded phd students only.

This project does not have funding attached. You will need to have your own means of paying fees and living costs and / or seek separate funding from student finance, charities or trusts.

Adjoint based optimization of vertical axis wind turbines

Software modelling and optimization for ai computing architectures, funded phd project (uk students only).

This research project has funding attached. It is only available to UK citizens or those who have been resident in the UK for a period of 3 years or more. Some projects, which are funded by charities or by the universities themselves may have more stringent restrictions.

Multi-Physics Optimization of Control Valve Structure – An Integrated approach with Approximation Assisted Models

Optimization and control of nonlinear and partial differential equations., machine learning assisted optimization techniques for fitting excitonic spin-orbit models to big data, development of data-driven design optimization framework for expensive real world engineering problems, competition funded phd project (students worldwide).

This project is in competition for funding with other projects. Usually the project which receives the best applicant will be successful. Unsuccessful projects may still go ahead as self-funded opportunities. Applications for the project are welcome from all suitably qualified candidates, but potential funding may be restricted to a limited set of nationalities. You should check the project and department details for more information.

Building Sustainability and Occupant Well-being: Data-Driven Design Optimization

Machine learning and ai for optical system optimization, funded phd project (european/uk students only).

This project has funding attached for UK and EU students, though the amount may depend on your nationality. Non-EU students may still be able to apply for the project provided they can find separate funding. You should check the project and department details for more information.

Simulation and optimization of the anaerobic digestion process for the production of renewable energy and valuable compounds from biodegradable wastes

Phd in thermal route optimization of predictive controls to improve bev efficiency using ai & ml, unmanned aerial vehicle thrust optimization with ducted propeller in various flight modes, design and performance optimization of proton exchange membrane fuel cell for aviation application, aerodynamic optimization of wind farms.

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Tepper School of Business

Algorithms, Combinatorics, and Optimization

Related to the Ph.D. program in operations research, Carnegie Mellon offers an interdisciplinary Ph.D. program in algorithms, combinatorics, and optimization. This program is administered jointly by the Tepper School of Business (operations research group), the Computer Science Department ( algorithms group ), and the Mathematics Department (discrete mathematics group).

Interdisciplinary Approach

To a great extent, the mathematics used by computer scientists and operations researchers overlap. The boundaries between operations research and computer science have become blurred. Important new theories and whole fields, like polyhedral combinatorics, have been and are being developed jointly by computer scientists, operations researchers, and applied mathematicians (who consider themselves a little bit of both). Presentations of new results on graphs and matroid theory can be heard at operations research conferences, while papers on linear programming, network flows, and matching in graphs are frequently presented at computer science conferences. The mathematical content of the papers has become greater and more diverse. Yet, in spite of this, few Ph.D. students graduate with an equally solid knowledge of all three areas.

The Ph.D. program in algorithms, combinatorics, and optimization is intended to fill this gap. It brings together the study of the mathematical structure of discrete objects and the design and analysis of algorithms in areas such as:

• Network Optimization
• Combinatorial Optimization
• Integer Programming
• Polyhedral Theory
• Computational Algebra
• Convex and Discrete Geometry
• Number Theory

Course of Study

The coordinating committee has established a challenging core curriculum in analysis, algebra, probability, combinatorics, linear and integer programming, graph theory, convex optimization, algorithms, and complexity theory. For more information, see the separate brochure for the Algorithms, Combinatorics, and Optimization program, or go to the ACO homepage.

P lease visit our Ph.D. Student Profiles page t o view the profiles of our current doctoral candidates.

Program details.

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• Building The Intelligent Future: Strategic Plan 2024-2030
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The Ohio State University

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Graduate-Programs-MS and PhD Operations Research

Operations research.

Operations Research (OR) applies advanced analytical methods to help make better decisions. Employing techniques such as:

• mathematical modeling,
• statistical analysis, and
• mathematical optimization

Operations research arrives at optimal or near-optimal solutions to complex decision-making problems.

The ISE Department at the Ohio State University has a premier graduate program in operations research. The research focus is both on:

• methodology (data analytics, optimization, and stochastic processes)
• applications (cloud computing, cyber and homeland security, energy systems, logistics and supply chain, social networks, sustainable mobility, water resources management)

Up to 3 University and College Scholarships and Fellowships are available for first-year PhD students. To be considered, please complete your application by November 30th .

To be considered for Department Teaching and Research Assistantships and Scholarships , please complete your application by January 1st.

Operations Research Degree Programs

The ISE department at the Ohio State University offers two degree programs (MS and PhD) in OR:

• Master of Science (MS) in OR builds fundamental OR skills with an emphasis on the application of these skills in practice
• Doctor of Philosophy (PhD) in OR is academically rigorous with an emphasis on scholarly research and achievement. PhD students are prepared for academic placements and research-oriented positions in government and industry

Graduates of the OR PhD program at the Ohio State University lead successful careers in:

• Academia: Air Force Institute of Technology, Bowling Green State, Korean Advanced Institute of Science and Technology, National University of Singapore, University of Alabama, University of Ghana Business School

Why Study Operations Research?

• One of the Best Business Jobs: Operations Research Analyst Ranked #2 Best Business Job. Source: U.S. News and World Report
• Increasing Job Opportunities: Operations Research Analyst (increase 22% by 2018) Management analyst (increase 24%) Computer systems analyst (increase 20%). Source: Bureau of Labor Statistics

Graduates of the OR MS and PhD programs at the Ohio State University lead successful careers in:

• Industry : American Woodmark Co., Bell Labs, Flexis North America, General Motors, Goodyear, Honda, J.P. Morgan Chase, Lightning Bolt Solutions, Pacific Gas and Electric, Qualcomm, SABRE, Samsung
• Government : Battelle Memorial Institute, Center for Naval Research, the Coast Guard

INFORMS Student Chapter at OSU

The Institute for Operations Research and the Management Sciences (INFORMS) is the largest society in the world for professionals in the field OR, Management Science, and Analytics.

The INFORMS Student Chapter at OSU serves as a forum to forge intellectual connections with faculty, students, alumni, and professionals that lead to publications, job opportunities, consulting relationships, and internships.

INFORMS Student Chapter at OSU activities include:

• OSU INFORMS Lecture Series
• Volunteering in regional workshops and conferences
• Tutorials on software (e.g., LaTeX, MATLAB, Cplex)
• Social events (e.g., monthly happy hours, potlucks)

Student Demographics : Female: 28% PhD: 45% MS: 55% (2018)

Operations Research Graduate Curriculum

• Optimization:  ISE 5200 Linear Optimization, ISE 7250 Operations Research Models and Methods
• Stochastic Processes:  ISE 6300 Simulation for System Analytics and Decision-Making
• Statistics:  ISE 5110 Forecasting, Regression, and Design of Engineering Experiments
• Optimization:  ISE 7200 Advanced Nonlinear Optimization
• Stochastic Processes:  ISE 7300 Stochastic Processes 
• Optimization:  ISE 5220 Complementarity Modeling and Applications (in Spring 2015, this course was offered as ISE 5194 (32873 and 32874)), ISE 6220 Network Optimization, ISE 6290 Stochastic Optimization, ISE 7210 Large-Scale Optimization, ISE 7230 Integer Optimization, ISE 7420 Sequencing and Scheduling
• Stochastic Processes:  ISE 5350 Probabilistic Models and Methods in Operations Research (in Spring 2015, this course was offered as ISE 5194 (32871 and 32872)), ISE 7100 Advanced Simulation 
• Optimization:  ISE 8299 Special Topics in Optimization. Topics can include: Heuristics and Global Optimization, Graphs and Networks 
• Stochastic Processes:  ISE 8399 Special Topics in Stochastic Processes. Topics can include: Queuing Networks ,Stochastic Control, Electricity Markets, Energy Systems , Water Management 
• ISE 5410 Quantitative Methods in Production and Distribution Logistics, ISE 5830 Decision Analysis, ISE 5840 Market Engineering

Prior to admission, students intent on graduate studies in operations research should be proficient in the following areas (Students without evidence of this material on their transcripts will have to demonstrate proficiency with the subject matter. This can be accomplished via appropriate coursework, at either the undergraduate or graduate level, to be determined in consultation with the academic adviser.):

• Vector calculus
• Optimization
• Calculus-based probability
• Probability-based statistics
• Linear algebra
• Computer programming (e.g., C, C++, Java)

All OR Graduate Students must satisfy degree requirements defined in the Industrial and Systems Engineering Graduate Student Handbook. Specific requirements for OR students include “OR Fundamentals,” “Non-OR ISE Fundamentals,” and a course sequence in an application area, as indicated below:

• OR Fundamentals: 5110, 5200, 6300, 7250, 7883 (2 semesters)
• Non-OR ISE Fundamentals: One 5000-level or higher ISE course in human factors or manufacturing engineering, subject to approval of the advisory committee
• Application Area: At least 3 units in an application, subject to approval of the advisory committee
• M.S. thesis
• pass the OR M.S. exit exam
• earn a B or higher in a 6000 or higherlevel course in operations research (in addition to OR fundamentals for MS students) that is at least 3 units and has a project requirement (more details are shown later)
• OR Fundamentals: 5110, 5200, 6300, 7200, 7250, 7300, 7883 (3 semesters)
• Application Area: At least 6 units in an application, subject to approval of the advisory committee
• Special Topics: Dedicated OR Ph.D. students are expected to take as many elective and special topics courses as their schedules permit

During the first three semesters, Ph.D. students are expected to identify a potential research topic of interest and a faculty adviser. Undertaking independent study (ISE 6193 or ISE 7193) is the recommended method of accomplishing this.

2.1 M.S. Exit Examination for ISE M.S. students studying operations research

• The M.S. Exit Examination is administered annually during the week after Spring final complete. Any ISE graduate student who achieves an overall GPA (including all courses taken at OSU) of 3.00 is eligible to take the exam. Those students who are planning to graduate in Fall should take the exam in the preceding Spring semester. The process to sign-up for the exam will be announced during Spring semester. Students intending to take the exam must sign-up before the announced deadline, so there is sufficient time to check that the grade eligibility requirement is satisfied.
• Optimization : Integer and Linear Programming Formulations and Solution Methods; Linear Programming Theory and Duality; Complexity Theory; Convexity
• Stochastic Processes : Random Variables; Probability Distributions; Conditional Probability and Expectations; Markov Chains; Random Number Generation; Simulation Theory
• Statistics : Parametric and Non-Parametric Hypothesis Testing; Distribution Fitting; Regression
• After the exams have been completed, the OR Faculty meet to discuss each student’s performance on the exam and performance in classes taken. Based on this, the faculty determine whether each student has “passed” or “failed” the examination.
• A student who has failed the examination, may be deemed eligible to retake it. Students who are deemed eligible to retake the exam must do so the next time that it is offered. No student will be eligible to take the exam more than twice.

2.2 A project-based operations research course with at least a B grade

• Student must earn a B or higher in a 6000 or higher-level course in operations research. This course must have a project requirement, and it must be at least 3 units.
• This course cannot be any of the OR fundamentals for M.S. students (ISE 6300, 7250).
• This course cannot be counted toward any of the other minimal degree requirements. For instance, this course cannot be the same as the only 3-unit course that is counted toward an application course. It cannot be a non-OR ISE course as well; observe that such a course is a non-OR course.
• The project must be done as an individual.
• ISE 6220 Network Optimization
• ISE 6290 Stochastic Optimization
• ISE 7100 Advanced Simulation
• ISE 7210 Large-Scale Optimization
• ISE 7230 Integer Optimization
• ISE 7420 Sequencing and Scheduling
• ISE 7300 Stochastic Processes
• An independent study with a report at the end.
• You may be asked to bring a copy of your project topic and report to make sure this requirement is fulfilled.

Both options 2.1 and 2.2 require a two-member committee for graduation by the graduate school. The first member of the committee should be the M.S. adviser. The second committee member is typically the professor who taught the project-based course in option 2.2, and the faculty coordinator for the OR M.S. Exit exam in option 2.1

Qualifying Examination for ISE Ph.D. students studying operations research

• Successful completion of the Ph.D. Qualifying Examination is a prerequisite for taking the Candidacy examination. Thus, students who do not pass the Qualifying Examination are not able pursue a Ph.D. in operations research.
• The OR Ph.D. Qualifying Examination is administered annually during the week after Spring finals complete.
• Any ISE graduate student who achieves a GPA of 3.30 or higher in the OR Fundamentals (ISE 5110, ISE 5200, ISE 6300, ISE 7200, ISE 7250, and ISE 7300) is eligible to take the exam. This GPA requirement pertains solely to courses taken at OSU. Students who have taken their “fundamentals” elsewhere are eligible to take the exam, provided that their OSU GPA in any remaining fundamentals courses taken at OSU is at least 3.30.
• Optimization : Integer, Linear, and Non-Linear Programming Formulations and Solution Methods; Linear and Non-Linear Programming Theory and Duality; Complexity Theory; Convexity
• Stochastic Processes : Random Variables; Probability Distributions; Conditional Probability and Expectations; Poisson Processes; Markov Chains; Random Number Generation; Simulation Theory; Basic Queuing Theory
• After the exams have been completed the OR Faculty meet to discuss each student’s performance on the exam, performance in classes taken, and academic and research interests and goals. Based on this, the faculty determine whether or not each student has “passed” or “failed” the examination.

Minor degree requirements

PhD students are required to complete 2 minors. Popular minors include:

• Computer Science
• Mathematics

• Youth Program
• Wharton Online

PhD Course Descriptions

Oidd9000 - foundations of dec proc (course syllabus).

The course is an introduction to research on normative, descriptive and prescriptive models of judgement and choice under uncertainty. We will be studying the underlying theory of decision processes as well as applications in individual group and organizational choice. Guest speakers will relate the concepts of decision processes and behavioral economics to applied problems in their area of expertise. As part of the course there will be a theoretical or empirical term paper on the application of decision processes to each student's particular area of interest.

OIDD9010 - Oid Faculty and Research (Course Syllabus)

This course introduces first-year Operations, Information and Decisions (OID) PhD students to OID Department faculty members and their research. The course is designed to meet once a week, both in the fall and the spring, allowing most (if not all) OID faculty to present to first-year PhD students either classic or current research in their fields of expertise. The course's goals are twofold. First, it seeks to introduce first-year PhD students to OID faculty in a substantive (as opposed to social) manner and to expose students to the breadth of research conducted in the department. Second, through early exposure, the course aims to pique students' interest in the department's foundational courses in decision making, information systems, and operations management.

OIDD9040 - Experimental Economics (Course Syllabus)

This course will help prepare you to run your own economics laboratory and field experiments. Experimental methods have been widely adopted by economists to develop new insights, and some economic theories and hypotheses are uniquely well-suited for testing with experimental tools and data. Achieving high internal and external validity requires careful experimental design. Substantive areas of application in the course will include market equilibrium, asset bubbles, learning in games, public good provision, and labor market relationships. Additional topics may include biases in individual decision-making; field experiments in development economics; and happiness, neuroeconomics, and behavioral/experimental welfare economics. Economists' typical interests in strategic and market-based interactions raise particular methodological challenges and opportunities.

OIDD9060 - Proseminar in Opim Resch (Course Syllabus)

Advanced seminar focusing on topics in Operations,Information and Decisions research

OIDD9100 - Intro Lin,Nonlin,Int Opt (Course Syllabus)

Introduction to mathematical optimization for graduate students who would like to be intelligent and sophisticated users of mathematical programming but do not necessarily plan to specialize in this area. Linear, integer and nonlinear programming are covered, including the fundamentals of each topic together with a sense of the state-of-the-art and expected directions of future progress. Homework and projects emphasize modeling and solution analysis, and introduce the students to a large variety of application areas.

OIDD9120 - Intro To Optimization (Course Syllabus)

This course constitutes the second part of a two-part sequence and serves as a continuation of the summer math camp. Mathematical optimization provides a unifying framework for studying issues of rational decision-making, optimal design, effective resource allocation and economic efficiency. It is a central methodology of many business-related disciplines, including operations research, marketing, accounting, economics, game theory and finance. In many of the disciplines, a solid background in optimization theory is essential for doing research. This course provides a rigorous introduction to the fundamental theory of optimization. It examines optimization theory in two primary settings: static optimization and optimization over time (dynamic programming). Applications from problem areas in which optimization plays a key role are also introduced. The goal of the course is to provide students with a foundation sufficient to use basic optimization in their own research work and/or to pursue more specialized studies involving optimization theory. The course is designed for entering doctoral students. The prerequisites are calculus, linear algebra and some familiarity with real analysis, as covered in summer math camp. Other concepts are developed as needed throughout the course.

Prerequisites: OIDD 9100

OIDD9130 - Lin Prog & Int Pnt Meth (Course Syllabus)

In-depth study of the theory and algorithms related to the solution of linear programming problems. Optimality conditions, duality and sensitivity analysis. Primal and dual simplex methods. Interior point methods. Large-scale optimization. Dantzig-Wolfe decomposition.

Prerequisites: OIDD 9100 OR ESE 5040

OIDD9140 - Advanced Non-Lin Progr (Course Syllabus)

Convex sets and functions. Tangent cones. Polar cones. Optimality conditions and duality theory. Methods for unconstrained and constrained optimization. Interior and exterior penalty methods. Lagrangean and augmented Lagrangean methods.

OIDD9150 - Graph Theory & Networks (Course Syllabus)

Deals mainly with algorithmic and computational aspects of graph theory. Topics and problems include reachability and connectivity, setcovering, graph coloring, location of centers, location of medians, trees, shortest path, circuits, traveling salesman problem, network flows, matching, transportation, and assignment problems.

OIDD9160 - Advanced Integer Progrmg (Course Syllabus)

In-depth review of solution methods: Lagrangean relaxation and column generation, Benders partitioning, cross-decomposition, surrogate relaxation, cutting planes and valid inequalities, logical processing, probing, branch-and-bound, branch-and-price. Study of special problems and applications: matching, location, generalized assignment, traveling salesman, forest planning, production scheduling. Prerequisite: OIDD 910/ESE 504 or equivalent. Please email the instructor for any questions regarding the prerequisite.

OIDD9200 - Empirical Research in Om (Course Syllabus)

Empirical research in Operations Management has been repeatedly called for over the last 10-15 years, including calls made from the academic thought leaders in the field as well as by many of the editors of the top academic journals. Remarkably though, most researchers in the field would be pressed to name even three empirical papers published in such journals like Management Science or Operations Research. But, has there really been so little published related to empirical Operations Management (you might be surprised to learn that all five bullets listed above has been addressed by Management Science papers)? What types of problems in operations are interesting and worthwhile studying from an empirical viewpoint? How can one get started with an empirical research project in Operations Management? These are the questions that are at the heart of this course. Specifically, the objective of this course is to (a) expose doctoral students to the existing empirical literature and (b) to provide them with the training required to engage in an empirical study themselves.

OIDD9300 - Stochastic Models I (Course Syllabus)

This course introduces mathematical models describing and analyzing the behavior of processes that exhibit random components. The theory of stochastic processes will be developed based on elementary probability theory and calculus. Topics include random walks, Poisson processes, Markov chains in discrete and continuous time, renewal theory, and martingales. Applications from the areas of inventory, production, finance, queueing and communication systems will be presented throughout the course.

Prerequisites: STAT 5100 OR STAT 5500

OIDD9310 - Stochastic Models II (Course Syllabus)

Extension of the material presented in OIDD930 to include renewal theory, martingales, and Brownian motion.

Prerequisites: OIDD 9300

OIDD9320 - Queuing Theory (Course Syllabus)

This course presents the mathematical foundations for the analysis of queueing systems. We will study general results like Little's law and the PASTA property. We will analyze standard queueing systems (Markovian systems and variations thereof) and simple queueing networks, investigate infinite server models and many server approximations, study GI/G/1 queues through random walk approximations, and read papers on applied queueing models.

OIDD9340 - Dynamic Programming (Course Syllabus)

The course goal is to provide a brief but fairly rigorous introduction to the formulation and solution of dynamic programs. Its focus is primarily methodological. We will cover discrete state space problems, over finite or infinite time horizon, with and without discounting. Structured policies and their theoretical foundation will be of particular interest. Computational methods and approximation methods will be addressed. Applications are presented throughout the course, such as inventory policies, production control, financial decisions, and scheduling.

OIDD9370 - Methods Stumblers (Course Syllabus)

This PhD-level course is for students who have already completed at least a year of basic stats/methods training. It assumes students already received a solid theoretical foundation and seeks to pragmatically bridge the gap between standard textbook coverage of methodological and statistical issues and the complexities of everyday behavioral science research. This course focuses on issues that (i) behavioral researchers are likely to encounter as they conduct research, but (ii) may struggle to figure out independently by consulting a textbook or published article.

OIDD9400 - Operations Mgmt (Course Syllabus)

Concepts, models, and theories relevant to the management of the processes required to provide goods or services to consumers in both the public and private sectors. Includes production, inventory and distribution functions, scheduling of service or manufacturing activities, facility capacity planning and design, location analysis, product design and choice of technology. The methodological basis for the course includes management science, economic theory,organization theory, and management information system theory.

OIDD9410 - Dist System Sem (Course Syllabus)

Seminar on distribution systems models and theory. Reviews current research in the development and solution of models of distribution systems. Emphasizes multi-echelon inventory control, logistics management, network design, and competitive models.

Prerequisites: OIDD 9400

OIDD9430 - Retail Operations (Course Syllabus)

Oidd9500 - perspect on info system (course syllabus).

Provides doctoral students in Operations and Information Management and other related fields with a perspective on modern information system methodologies, technologies, and practices. State-of-the-art research on frameworks for analysis, design, and inplementation of various types of information systems is presented. Students successfully completing the course should have the skills necessary to specify and implement an information system to support a decision process.

OIDD9510 - Seminar On Logic Mdlng (Course Syllabus)

Seminar on the elements of formal logic necessary to read and contribute to the Logic modeling literature, as well as the implementation principles for logic models. The primary topics include elements of sentence and predicate logic, elements of modal logics, elements of semantics, mechanical theorem proving, logic and database, nonmonotonic reasoning, planning and the frame problem, logic programming, and metainterpreters. Permission of the instructor and some prior knowledge of logic or Prolog.

OIDD9520 - Computational Game Thry (Course Syllabus)

Seminar on principles of knowledge-based systems including expert systems. Topics include basics of expert systems, knowledge representation, meta-level reasoning, causal reasoning, truth maintenance systems, model management, planning systems and other applications. Permission of instructor and knowledge of logic and Prolog or Lisp.

OIDD9530 - Explaining Explanation (Course Syllabus)

In the social sciences we often use the word "explanation" as if (a) we know what we mean by it, and (b) we mean the same thing that other people do. In this course we will critically examine these assumptions and their consequences for scientific progress. In part 1 of the course we will examine how, in practice, researchers invoke at least three logically and conceptually distinct meanings of "explanation:" identification of causal mechanisms; ability to predict (account for variance in) some outcome; and ability to make subjective sense of something. In part 2 we will examine how and when these different meanings are invoked across a variety of domains, focusing on social science, history, business, and machine learning, and will explore how conflation of these distinct concepts may have created confusion about the goals of science and how we evaluate its progress. Finally , in part 3 we will discuss some related topics such as null hypothesis testing and the replication crisis. We will also discuss specific practices that could help researchers clarify exactly what they mean when they claim to have "explained" something, and how adoption of such practices may help social science be more useful and relevant to society.

OIDD9550 - Research Sem in Info Sys (Course Syllabus)

This course provides an overview of some of the key Information Systems literature from the perspective of Insormation Strategy and Economics (ISE) and Information Decision Technologies (IDT). This course is intended to provide an introduction for first year OIDD doctoral students, as well as other Wharton doctoral students, to important core research topics and methods in ISE and IDT in order for students to do research in the field of Information Systems. While it is intended as a "first course" for OPIM doctoral students in ISE and IDT, it may also be useful for students who are engaged in research or plan to perform information technology related research in other disciplines.

OIDD9600 - Res Sem in Info Tech (Course Syllabus)

Explores economic issues related to information technology, with emphasis on research in organizational or strategic settings. The course will follow a seminar format, with dynamically assigned readings and strong student contribution during class sessions (both as participant and, for one class, as moderator.)

OIDD9610 - Research Seminar in Isse (Course Syllabus)

This is the advanced doctoral-level research research in information strategy and economics that builds on the foundations developed in OPIM960. Much of the content will be focused on current research areas in information strategy such as the information and organizational economics, information technology and firm performance, search cost and pricing, information and incentives, coordination costs and the boundary of the firm, and the economics of information goods (including pricing and intellectual property protection). In addition, promising empirical approaches such as the use of intelligent agents for data collection or clickstream data analysis will be discussed.

OIDD9890 - Topics in Oidd (Course Syllabus)

The specific content of this course varies form semester to semester, depending on student and faculty interests.

OIDD9920 - Conflict Mgmt Seminar (Course Syllabus)

This seminar exposes students to the central issues in conflict management research. This course covers both analytic and behavioral perspectives of conflict management, and describes how the field has developed. Through discussions of theory and empirical research, the course aims to develop a foundation for understanding the extant literature and how common methodological tools have shaped the types of questions conflict management scholars have investigated - and neglected.

OIDD9999 - OIDD 9999 (Course Syllabus)

Independent Study

PhD Program

• Program of Study
• Course Requirements
• Details on Program Milestones
• Learning, Research, and Working at Wharton
• Financial Aid and Stipends
• Living in Philadelphia
• Post-Wharton

Course Information

• Course Descriptions
• Course Schedule

Algorithms, Combinatorics and Optimization (ACO)

Carnegie Mellon University offers an interdisciplinary Ph.D program in Algorithms, Combinatorics, and Optimization (ACO). 

This program is the first of its kind in the United States. It is administered jointly by the  Tepper School of Business  (Operations Research group), the  Computer Science Department  ( Theory & Algorithms & Complexity Groups ), and the  Department of Mathematical Sciences  (Discrete Mathematics group).

The mathematics used by computer scientists and operations researchers overlap to a large extent. The boundaries between Operations Research and Computer Science have become blurred. Important new theories and whole fields, like polyhedral combinatorics, have been and are being developed jointly by computer scientists, operations researchers, and applied mathematicians who consider themselves a little bit of both. Presentations of new results on graphs and matroid theory can be heard at Operations Research conferences, while papers on linear programming, network flows, and matchings in graphs are frequently presented at Computer Science conferences. The mathematical content of the papers has become greater and more diverse. Yet, in spite of this, few Ph.D students graduate with an equally solid knowledge of all three areas.

The Ph.D program in Algorithms, Combinatorics, and Optimization at Carnegie Mellon is intended to fill this gap. The program brings together the study of the mathematical structure of discrete objects and the design and analysis of algorithms in areas such as graph theory, combinatorial optimization, integer programming, polyhedral theory, computational algebra, geometry, and number theory.

How to Apply

You may apply to the Ph.D. Program in Algorithms, Combinatorics, and Optimization through any of the three participating departments.

To apply for the ACO program though the Computer Science Department you need to apply via the  School of Computer Science  online application . Apply for the Ph.D. in Computer Science and  select the interdisciplinary program in the appropriate section of the online application .

Applicants will be selected for admission by the ACO faculty in consultation with committees in each home department. Financial support for students admitted into this program is available under the same conditions as for the other Ph.D. Programs at Carnegie Mellon.

• Current Semester Courses
• Upcoming Semester Courses
• Schedule of Classes
• Undergraduate Catalog
• Bachelor's Programs
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• Ph.D. in Computer Science
• Ph.D. in ACO
• Ph.D. in PAL
• CNBC Certificate Program
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• Doctoral - How to Apply
• Degrees Conferred
• Other SCS Doctoral Programs
• Student Resources

AI, machine learning, optimization

Control & Optimization: Optimal design and engineering systems operation methodologies are applied to various domains, including integrated circuits, vehicles and autopilots, energy systems (such as storage, generation, distribution, and smart devices), wireless networks, and financial trading. Optimization is also widely used in signal processing, statistics, and machine learning as a method for fitting parametric models to observed data. Examples include:

Languages and solvers for convex optimization, distributed convex optimization, robotics, smart grid algorithms, learning via low-rank models, approximate dynamic programming, methods for sparse signal recovery, dynamic game theory, control theory, decentralized control, and imaging systems.

Machine Learning: Our research in machine learning spans traditional methods and advanced deep learning techniques, with a focus on both theoretical foundations and practical applications. Examples include:

• Supervised learning,
• Unsupervised learning,
• Reinforcement learning,
• Various applications

Signal Processing & Multimedia: Extracting or recovering useful information while reducing unwanted noise is achieved through sophisticated mathematical methods and computational techniques to process signals (such as audio, video, electromagnetic, biomedical, remote sensing, multimedia, and others). Applications include multimedia compression, communications, networked media systems, augmented reality, radar and remote sensing, neuroscience, and biomedical systems. In addition to using theoretical analyses and systematic experiments to study the underlying principles, we often build real‐time test beds and prototypes to validate and demonstrate our ideas. Examples include:

• Image and video coding
• Media streaming
• Augmented and virtual reality
• Compact descriptors for visual search
• Personalized and immersive media
• Computational imaging and display
• Remote sensing of the Earth and other planets
• Sensors for driverless cars
• Signal processing for neuroscience and biomedicine

Algorithms, Combinatorics, and Optimization (Ph.D.)

Focus: furthering the study of discrete structures in the context of computer science, applied mathematics, and operations research.

Smart. Open. Grounded. Inventive. Read our Ideas Made to Matter.

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Combine an international MBA with a deep dive into management science. A special opportunity for partner and affiliate schools only.

A doctoral program that produces outstanding scholars who are leading in their fields of research.

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Apply now and work for two to five years. We'll save you a seat in our MBA class when you're ready to come back to campus for your degree.

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PhD Program

Program overview.

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Rigorous, discipline-based research is the hallmark of the MIT Sloan PhD Program. The program is committed to educating scholars who will lead in their fields of research—those with outstanding intellectual skills who will carry forward productive research on the complex organizational, financial, and technological issues that characterize an increasingly competitive and challenging business world.

Start here.

Learn more about the program, how to apply, and find answers to common questions.

Admissions Events

Check out our event schedule, and learn when you can chat with us in person or online.

Start Your Application

Visit this section to find important admissions deadlines, along with a link to our application.

Click here for answers to many of the most frequently asked questions.

PhD studies at MIT Sloan are intense and individual in nature, demanding a great deal of time, initiative, and discipline from every candidate. But the rewards of such rigor are tremendous:  MIT Sloan PhD graduates go on to teach and conduct research at the world's most prestigious universities.

PhD Program curriculum at MIT Sloan is organized under the following three academic areas: Behavior & Policy Sciences; Economics, Finance & Accounting; and Management Science. Our nine research groups correspond with one of the academic areas, as noted below.

MIT Sloan PhD Research Groups

Behavioral & policy sciences.

Economic Sociology

Institute for Work & Employment Research

Organization Studies

Technological Innovation, Entrepreneurship & Strategic Management

Economics, Finance & Accounting

Accounting  

Management Science

Information Technology

System Dynamics  

Those interested in a PhD in Operations Research should visit the Operations Research Center .  

PhD Program Structure

Additional information including coursework and thesis requirements.

MIT Sloan Predoctoral Opportunities

MIT Sloan is eager to provide a diverse group of talented students with early-career exposure to research techniques as well as support in considering research career paths.

Rising Scholars Conference

The fourth annual Rising Scholars Conference on October 25 and 26 gathers diverse PhD students from across the country to present their research.

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The goal of the MIT Sloan PhD Program's admissions process is to select a small number of people who are most likely to successfully complete our rigorous and demanding program and then thrive in academic research careers. The admission selection process is highly competitive; we aim for a class size of nineteen students, admitted from a pool of hundreds of applicants.

What We Seek

• Outstanding intellectual ability
• Excellent academic records
• Previous work in disciplines related to the intended area of concentration
• Strong commitment to a career in research

MIT Sloan PhD Program Admissions Requirements Common Questions

Dates and Deadlines

Admissions for 2024 is closed. The next opportunity to apply will be for 2025 admission. The 2025 application will open in September 2024. 

More information on program requirements and application components

Students in good academic standing in our program receive a funding package that includes tuition, medical insurance, and a fellowship stipend and/or TA/RA salary. We also provide a new laptop computer and a conference travel/research budget.

Funding Information

Throughout the year, we organize events that give you a chance to learn more about the program and determine if a PhD in Management is right for you.

PhD Program Events

Docnet recruiting forum at university of minnesota.

We will be joining the DocNet consortium for an overview of business academia and a recruitment fair at University of Minnesota, Carlson School of Management.

September 25 PhD Program Overview

During this webinar, you will hear from the PhD Program team and have the chance to ask questions about the application and admissions process.

DocNet Recruiting Forum - David Eccles School of Business

MIT Sloan PhD Program will be joining the DocNet consortium for an overview of business academia and a recruitment fair at Utah, David Eccles School of Business.

October PhD Program Overview

Complete PhD Admissions Event Calendar

Unlike formulaic approaches to training scholars, the PhD Program at MIT Sloan allows students to choose their own adventure and develop a unique scholarly identity. This can be daunting, but students are given a wide range of support along the way - most notably having access to world class faculty and coursework both at MIT and in the broader academic community around Boston.

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Profiles of our current students

MIT Sloan produces top-notch PhDs in management. Immersed in MIT Sloan's distinctive culture, upcoming graduates are poised to innovate in management research and education.

Academic Job Market

Doctoral candidates on the current academic market

Academic Placements

Graduates of the MIT Sloan PhD Program are researching and teaching at top schools around the world.

view recent placements 

MIT Sloan Experience

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The PhD Program is integral to the research of MIT Sloan's world-class faculty. With a reputation as risk-takers who are unafraid to embrace the unconventional, they are engaged in exciting disciplinary and interdisciplinary research that often includes PhD students as key team members.

Research centers across MIT Sloan and MIT provide a rich setting for collaboration and exploration. In addition to exposure to the faculty, PhD students also learn from one another in a creative, supportive research community.

Throughout MIT Sloan's history, our professors have devised theories and fields of study that have had a profound impact on management theory and practice.

From Douglas McGregor's Theory X/Theory Y distinction to Nobel-recognized breakthroughs in finance by Franco Modigliani and in option pricing by Robert Merton and Myron Scholes, MIT Sloan's faculty have been unmatched innovators.

This legacy of innovative thinking and dedication to research impacts every faculty member and filters down to the students who work beside them.

Faculty Links

• Accounting Faculty
• Economic Sociology Faculty
• Finance Faculty
• Information Technology Faculty
• Institute for Work and Employment Research (IWER) Faculty
• Marketing Faculty
• Organization Studies Faculty
• System Dynamics Faculty
• Technological Innovation, Entrepreneurship, and Strategic Management (TIES) Faculty

Student Research

“MIT Sloan PhD training is a transformative experience. The heart of the process is the student’s transition from being a consumer of knowledge to being a producer of knowledge. This involves learning to ask precise, tractable questions and addressing them with creativity and rigor. Hard work is required, but the reward is the incomparable exhilaration one feels from having solved a puzzle that had bedeviled the sharpest minds in the world!” -Ezra Zuckerman Sivan Alvin J. Siteman (1948) Professor of Entrepreneurship

Sample Dissertation Abstracts - These sample Dissertation Abstracts provide examples of the work that our students have chosen to study while in the MIT Sloan PhD Program.

We believe that our doctoral program is the heart of MIT Sloan's research community and that it develops some of the best management researchers in the world. At our annual Doctoral Research Forum, we celebrate the great research that our doctoral students do, and the research community that supports that development process.

The videos of their presentations below showcase the work of our students and will give you insight into the topics they choose to research in the program.

Attention To Retention: The Informativeness of Insiders’ Decision to Retain Shares

2024 PhD Doctoral Research Forum Winner - Gabriel Voelcker

Watch more MIT Sloan PhD Program  Doctoral Forum Videos

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Doctoral Programs in Computational Science and Engineering

Doctor of philosophy in computational science and engineering, program requirements.

Programs Offered by CCSE in Conjunction with Select Departments in the Schools of Engineering and Science

The interdisciplinary doctoral program in Computational Science and Engineering ( PhD in CSE + Engineering or Science ) offers students the opportunity to specialize at the doctoral level in a computation-related field of their choice via computationally-oriented coursework and a doctoral thesis with a disciplinary focus related to one of eight participating host departments, namely, Aeronautics and Astronautics; Chemical Engineering; Civil and Environmental Engineering; Earth, Atmospheric and Planetary Sciences; Materials Science and Engineering; Mathematics; Mechanical Engineering; or Nuclear Science and Engineering.

Doctoral thesis fields associated with each department are as follows:

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As with the standalone CSE PhD program, the emphasis of thesis research activities is the development of new computational methods and/or the innovative application of state-of-the-art computational techniques to important problems in engineering and science. In contrast to the standalone PhD program, however, this research is expected to have a strong disciplinary component of interest to the host department.

The interdisciplinary CSE PhD program is administered jointly by CCSE and the host departments. Students must submit an application to the CSE PhD program, indicating the department in which they wish to be hosted. To gain admission, CSE program applicants must receive approval from both the host department graduate admission committee and the CSE graduate admission committee. See the website for more information about the application process, requirements, and relevant deadlines .

Once admitted, doctoral degree candidates are expected to complete the host department's degree requirements (including qualifying exam) with some deviations relating to coursework, thesis committee composition, and thesis submission that are specific to the CSE program and are discussed in more detail on the CSE website . The most notable coursework requirement associated with this CSE degree is a course of study comprising five graduate subjects in CSE (below).

Computational Concentration Subjects

Note: Students may not use more than 12 units of credit from a "meets with undergraduate" subject to fulfill the CSE curriculum requirements

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Research Area: Optimization

Research area:

Raed Al Kontar

Associate Professor

Saif Benjaafar

Seth Bonder Collegiate Professor

Albert S. Berahas

Assistant Professor

Aaresh Bhathena

Ph.D. Student

Robert Bordley

Professor of Practice

Yavuz A. Bozer

Changxiao Cai

Ralph L. Disney Professor, Director of Masters Programs

Amy M. Cohn

Arthur F. Thurnau Professor

Mark S. Daskin

Clyde W. Johnson Collegiate Professor Emeritus

Brian Denton

Stephen M. Pollock Collegiate Professor of Industrial and Operations Engineering

Marina Epelman

Professor, Associate Chair of Graduate Education

Juan-Alberto Estrada-Garcia

PhD Student

Salar Fattahi

Luis Garcia-Guzman

Teaching Professor

Leena Ghrayeb

PhD Candidate

The Ohio State University

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Joel Paulson Laboratory for Advanced Optimization and Control

We develop new learning-based theory and algorithms for optimization and control of complex systems under uncertainty, with applications in next-generation biochemical systems.

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• Group Members
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.cls-1{fill:#a91e22;}.cls-2{fill:#c2c2c2;} double-arrow About

Our research focuses on improving the quality, efficiency, and sustainability of engineered products and processes through the development of advanced decision-making strategies in the presence of uncertainty.

Professor Paulson specializes in formulating these strategies in terms of stochastic mathematical optimization problems that can be applied to a broad range of applications, with a particular emphasis on chemical and biological systems, as well as developing algorithms that can efficiently solve these problems. 

• Chemical Process Dynamics and Control (CBE 4624), Fall 2019 
• Neural Networks and Deep Learning (online CPDA program), Spring 2020

• Ph.D., MIT, 2016
• M.S. CEP, MIT, 2013
• B.S., University of Texas at Austin, 2011

Joel Paulson received his PhD in 2016 from the Massachusetts Institute of Technology (MIT), where he won an NSF Graduate Research Fellowship and multiple awards for research and outstanding teaching and mentoring.

His advisors were Professors Richard Braatz and Michael Strano. After completing his PhD, Dr. Paulson held a postdoctoral research position in Professor Ali Mesbah's group at the University of California, Berkeley.

While at UC Berkeley, he was a finalist for the 2017 International Federation of Automatic Control (IFAC) Conference Best Paper Award.

Professor Paulson has published several book chapters and over a dozen articles in such peer-reviewed journals as  ACS Nano , Journal of Physical Chemistry Letters , Organic Process Research & Development , Journal of Process Control , and International Journal of Robust and Nonlinear Control .

KEY DISTINCTIONS

• NSF CAREER Award, 2023
• Winner, Application Paper Prize at IFAC World Congress, 2020
• Finalist for Young Author Prize at IFAC World Congress, 2017 National Science Foundation Graduate Research Fellowship, 2011-2016
• Director’s Student Presentation Award Finalist, AIChE CAST division, 2016
• School of Engineering Graduate Student Award for Extraordinary Teaching and Mentoring, MIT, 2015  (only 1 chosen per year across all departments)
• Outstanding Graduate Teaching Assistant Award, Chemical Engineering, MIT, 2015 Goodwin Medal Nominee, MIT, 2015
• Robert T. Haslam Fellowship, MIT, 2015
• Best Poster Presentation Award, Chemical Engineering, UT Austin, 2011 National Merit Scholarship, 2008
• Semifinalist, Siemens Research Competition, 2007

University of Texas at Austin :

• David H. Koch (1962) Fellow 2011 Best Poster Presentation Award, 2011. (Winner from over 50 posters.)
• TAMS Research Scholarship, 2007
• Bobby Bragan Scholarship, 2004
• Artemys Foods – discussions on sustainable process development (2019)
• Owens Corning – discussions on process optimization (2020)
• Mitsubishi Electric Research Laboratories – discussions on Bayesian optimization (2021-date)

Related News

FAST UNCERTAINTY PROPAGATION AND PARAMETER ESTIMATION IN COMPUTATIONALLY INTENSIVE GENOME-SCALE BIOLOGICAL MODELS USING MACHINE LEARNING

i. Construction and validation of mathematical models is biological systems involving genome-scale molecular networks is a very challenging problem. The task of uncertainty quantification (UQ) represents: (i) calibrating the model with experimental data and (ii) propagating uncertainties through the model to characterize the quality of the model predictions. Although many methods for UQ have been developed, the majority of them are intractable on experiment-to-evaluate computational models. I developed a novel metamodeling approach that can vastly accelerate UQ methods for dynamic genome-scale biological system models in the presence of high-throughput experimental data.

i. Modeling is known to have a big impact on process understanding and optimization; however, unless the accuracy of the model is rigorously understood, then the impact of the model is limited. Thus, the developed method helps to answer this question of accuracy. In particular, most process models are functions of several unknown parameters (such as heat transfer coefficients or rate constants) that must be estimated from data. Once this has been done using the proposed approach, we can easily decide if more experiments are required or even which experiments to perform in the future to gain a better understanding of the process.

ii. We applied the method to infer extracellular kinetic parameters in a batch fermentation reactor consisting of diauxic growth on E. coli on a glucose/xylose mixed media. To the best of our knowledge, due to the complexity of the model, this problem had been unable to be solved in the literature using standard methods. Our novel metamodel enabled this problem to be solved a factor of more than 800 times faster and provided significant physical insights that had previously been unknown (such as the reported data set was insufficient for uniquely estimating all parameters).

• J.A. Paulson, M. Martin-Casas, and A. Mesbah. Fast uncertainty quantification for dynamic flux balance analysis using non-smooth polynomial chaos expansions. PLOS Computational Biology, 15, e1007308, 2019.

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.cls-1{fill:#a91e22;}.cls-2{fill:#c2c2c2;} double-arrow Group Members

Current members.

• Godstand Aimiuwu ,  [email protected]  2023-date
• Godstand Aimiuwu earned his B.Eng. degree in Chemical Engineering from the University of Benin, Nigeria, in 2017. Post-graduation, he secured a position as a Senior Process Engineer at the Dangote Petroleum Refinery and Petrochemicals, while also serving as a part-time consultant focused on the design and troubleshooting of chemical processes. Currently, he’s a second-year Ph.D. student in the Chemical Engineering department at Ohio State University and recently became a member of Jessica Winter and Paulson's group, with an aim to learn the techniques of Bayesian Optimization in Scalable Nanomanufacturing. 
• Nate Massa,  [email protected]  2023-date
• Nate Massa received his B.S. in Chemical Engineering from the University of Iowa in 2023 and is a second-year PhD graduate student in Chemical Engineering at The Ohio State University. During his undergraduate studies Nate worked in a high atmosphere aerosol experimental laboratory under Dr. Stanier, mostly performing data analysis and visualization to help draw conclusions from experiments. Nate just joined the Paulson group this year and is excited to learn methods of computational black and grey box optimization. 

• Kevin Donnelly,  [email protected]  2022-date
• Kevin Donnelly received his B.S. in Chemical Engineering (summa cum laude) from West Virginia University in 2022 with a minor in Law & Legal Studies. He began his Ph.D. work at The Ohio State University (OSU) in Fall 2022 under the co-advisory of Dr. Joel Paulson (OSU) and Dr. Bhavik Bakshi (ASU). His work is focused on climate-resistant process design of the food-energy-water nexus and data-driven optimization methods.  

• Madhav Reddy ,  [email protected]  2022-date
• Madhav Reddy Muthyala is a third-year master's student who is transitioning to a Ph.D. program from Spring 2024 under the guidance of Dr. Paulson. He earned his B.Tech in Chemical Engineering from Jawaharlal Nehru Technological University, Hyderabad in 2020. Prior to commencing his studies at OSU, he gained professional experience in the fields of machine learning and software development. Currently, his research focuses on the development of interpretable machine learning models for advancing next-generation materials discovery, as well as high-dimensional machine learning and uncertainty quantification.

• Wei-Ting (Jonathan) Tang ,  [email protected]  2022-date
• Wei-Ting (Jonathan) Tang is a third-year PhD student in Dr. Paulson’s group. He received B.S. and M.S. in Chemical Engineering at National Taiwan University (NTU) from 2020 and 2022. He did research at the Process System Engineering lab at NTU before joing the group, in which he focused on optimization of distillation processes. Currently, his research mainly focuses on development of deterministic global optimization algorithm for Gaussian Processes, Bayesian based novelty search algorithm, multi-fidelity Bayesian optimization, and application of Bayesian optimization to chemical reactor design. 
• Personal Website

• Ting Yeh Chen , [email protected] 2021-date
• Ting-Yeh Chen received her B.S. and M.S. in Chemical & Material Science Engineering from National Central University, Taiwan in 2019. She starts her Ph.D. journey at The Ohio State University in Fall 2021 advised by Dr. Joel Paulson. Her research focus on uncertainty quantification, closed-loop experimental design and machine learning & image analysis for bio-systems. 

• Akshay Kudva ,  [email protected]   2020-date
• Akshay Kudva received his B.tech in Chemical Engineering from Vellore Institute of Technology, Vellore in 2018, and M.tech with a specialization in Process Design Engineering from the University of Petroleum and Energy Studies (with highest honors) in 2020. Prior to joining OSU in 2020, he worked on mathematical optimization of process designs in pulp and fibre manufacturing industry. His present research revolves around multi-level optimization for decision making in the presence of uncertainty.    

• Farshud Sorourifar - [email protected]   2020-date
• Farshud Sorourifar is a National Science Foundation Graduate Research Fellow pursuing a Ph.D. advised by Professor Paulson. He received his B.S. in chemical engineering from the University of California, Berkeley, in 2020, and his M.S. in chemical engineering from the Ohio State University in 2023. During his tenure as a graduate student, he has held appointments at the Dow Chemical Company, Mitsubishi Electric Research Laboratories, and NASA's Quantum Artificial Intelligence Laboratories. His research is the the area of decision-making under uncertainty, which considers optimization and controls for applications in materials discovery, quantum computing, and next-generation energy and process systems. 

• Cong Wen (Kevin) Lu , [email protected]   2019-date
• Kevin Lu is 5th PhD candidate with a focus on greybox optimization – algorithms that integrated both physics-based and data-driven models in the presence of constraints and uncertainty. He received his Bachelors in Chemical Engineering from the University of Texas at Austin in 2019, and a Masters in Chemical Engineering from OSU in 2021. In addition to his research, Kevin has engaged many leadership activities, including: Chemical Engineering Graduate Council (CEGC), Council of Graduate Student (CGS), and COAM. 

2024/04/11 - Lowrie Banquet

2023/09/30 - West Fest

2023/09/03 - BBQ at Dr. Paulson's house

2023/05/06 - Hiking with Bakshi's group @ Cuyahoga Valley Natl Park

2023/03/23 - Lowrie Banquet

July 31, 2024 Collaborating to solve complex sustainability challenges: Paulson, Zhai, and Fan

July 1, 2024 Joel Paulson featured in Chemical Engineering Progress (CEP)

April 18, 2024 Graduate students recognized for teaching and organizational leadership

October 2, 2023 Jain, Paulson honored as trailblazers in AIChE's "35 Under 35"

January 17, 2023 Joel Paulson receives prestigious NSF CAREER Award

May 3, 2022 College celebrates 2022 Distinguished Faculty Award honorees

September 23, 2020 NSF funds additional cutting-edge projects led by Bhavik Bakshi

September 17, 2020 Chemical engineering department wins two high-profile NSF grants in same day

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3.  E. Harinath, L.C. Foguth, J.A. Paulson, and R.D. Braatz. Model predictive control of polynomial systems. In Handbook of Model Predictive Control , edited by Saša V. Raković and William S. Levine, Birkhäuser, 221-237, 2019.

2.  J.A. Paulson, E. Harinath, L.C. Foguth, and R.D. Braatz, Control and systems theory for advanced manufacturing. In Emerging Applications of Control and Systems Theory , edited by R. Tempo, S. Yurkovich, P. Misra, Springer, 63-79, 2018.

1.  J.A. Paulson, S. Streif, R. Findeisen, R.D. Braatz, and A. Mesbah. Fast stochastic model predictive control of end-to-end continuous pharmaceutical manufacturing. In Process Systems Engineering for Pharmaceutical Manufacturing , edited by Ravendra Singh and Zhihong Yuan, Elsevier, Amsterdam, Netherlands, Chapter 14, pages 353-378, 2018.

19.   A.D. Bonzanini, J.A. Paulson , G. Makrygiorgos, and A. Mesbah. Fast approximate learning-based multistage nonlinear model predictive control using Gaussian processes and deep neural networks. Computers & Chemical Engineering (accepted).

18.  A. Mesbah, J.A. Paulson , and R.D. Braatz. An internal model control design method for failure- tolerant control with multiple objectives. Computers & Chemical Engineering , 4:106955, 2020.

17.  J.A. Paulson  and A. Mesbah. Optimal Bayesian experiment design for nonlinear dynamic systems with chance constraints. Submitted to Journal of Process Control.

16. A. Mesbah, J.A. Paulson , and R. D. Braatz. An internal model control design method for multi-objective failure-tolerant control. Submitted to Journal of Process Control .

15.  J.A. Paulson , L. C. Foguth, Y. Peng, A. Mesbah, and R. D. Braatz. Optimization methods for fast model predictive control. Submitted to Control Systems Magazine .

14.  J.A. Paulson , T. L. M Santos, and A. Mesbah. Mixed stochastic-deterministic tube MPC for offset-free tracking in the presence of plant-model mismatch. Journal of Process Contro l, 2018 (in press).

13. T. A. N. Heirung, J.A. Paulson , S. Lee, and A. Mesbah. Model predictive control with active learning under model uncertainty: when, why, and how? AIChE Journa l, 64:3071–3081, 2018.

12. D. Gidon, B. Curtis, J.A. Paulson , D. B. Graves, and A. Mesbah. Model-based feedback control of a kHz-excited atmospheric pressure plasma jet. IEEE Transactions on Radiation and Plasma Medical Sciences , 2:129–137, 2018.

11. T. A. N. Heirung, J.A. Paulson , J. O’Leary, and A. Mesbah. Stochastic model predictive control-how does it work? Computers & Chemical Engineering , 114:158–170, 2018.

10. J.A. Paulson  and A. Mesbah. An efficient method for stochastic optimal control with joint chance constraints for nonlinear systems. International Journal of Robust and Nonlinear Control , 2017.

9. A. Mesbah, J.A. Paulson , R. Lakerveld, and R. D. Braatz. Model predictive control of an integrated continuous pharmaceutical manufacturing pilot plant. Organic Process Research & Development , 21:844–854, 2017.

8.  J.A. Paulson , M. Martin-Casas, and A. Mesbah. Input design for online fault diagnosis of nonlinear systems with stochastic uncertainty. Industrial & Engineering Chemistry Research , 56:9593–9605, 2017.

7.  J.A. Paulson , E. A. Buehler, R. D. Braatz, and A. Mesbah. Stochastic model predictive control with joint chance constraints. International Journal of Control , 1–14, 2017.

6. D. O. Bellisario, J.A. Paulson , R. D. Braatz, and M. S. Strano. An analytic solution for exciton generation, reaction, and diffusion in nanotube and nanowire-based solar cells. The Journal of Physical Chemistry Letters , 7:2683–2688, 2016.

5. M. Wang and J.A. Paulson . An adaptive model predictive control strategy for nonlinear distributed parameter systems using the Type-2 Takagai-Sugeno model. International Journal of Fuzzy System s, 18:792–805, 2015.

4. B. Jiang, X. Zhu, D. Huang, J.A. Paulson , and R. D. Braatz. A combined canonical variate analysis and fisher discriminant analysis (CVA–FDA) approach for fault diagnosis. Computers & Chemical Engineering , 77:1–9, 2015.

3. Y. Son, Q. H. Wang, J.A. Paulson , C. Shih, K. Tvrdy, B. AlFeeli, R. D. Braatz, M. S. Strano. Layer number dependence of MoS2 photoconductivity using photocurrent spectral atomic force microscope imaging. ACS Nano , 9:2843–2855, 2015.

2.  J.A. Paulson , A. Mesbah, X. Zhu, M. Molaro, and R. D. Braatz. Control of self-assembly in micro- and nano-scale systems. Journal of Process Control , 27:38–49, 2015.

1. D. A. Slanac, A. Lie, J.A. Paulson , K. J. Stevenson, and K. P. Johnston. Bifunctional catalyst for alkaline ORR via promotion of ligand and ensemble effects at Ag/MnOx nanodomains. The Journal of Physical Chemistry C , 116:11032–11039, 2012

Peer Reviewed Proceedings Publications

21.  J.A. Paulson  , T. A. N. Heirung, and A. Mesbah. Tube-based robust nonlinear model predictive control with guaranteed fault tolerance. Submitted to Proc. of ACC .

20.  J.A. Paulson   and A. Mesbah. Arbitrary polynomial chaos for quantification of general probabilistic uncertainties: Shaping closed-loop behavior of nonlinear systems. In Proc. of the IEEE Conference on Decision and Control , 2018 (accepted).

19.  J.A. Paulson   and A. Mesbah. Nonlinear model predictive control with explicit backoffs for stochastic systems under arbitrary uncertainty. In Proc. of the IFAC Conference on Nonlinear Model Predictive Control , pages 622–633, Madison, WI, August 2018.

18. T. L. M. Santos, J.A. Paulson  , and A. Mesbah. Offset-free stochastic model predictive control with enlarged feasibility region. In Proc. of the American Control Conference , pages 742–748, Milwaukee, WI June 2018.

17.  J.A. Paulson  , T. A. N. Heirung, R. D. Braatz, and A. Mesbah. Closed-loop active fault diagnosis for stochastic linear systems. In Proc. of the American Control Conference , pages 735–741, Milwaukee, WI June 2018.

16.  J.A. Paulson  , E. Buehler, and A. Mesbah. Arbitrary polynomial chaos for uncertainty propagation of correlated random variables in dynamic systems. In Proc. of the IFAC World Congress , pages 3607–3612, Toulouse, France, July 2017.

15.  J.A. Paulson  , L. Xie, and A. Mesbah. Offset-free robust MPC of systems with mixed stochastic and deterministic uncertainty. In Proc. of the IFAC World Congress , pages 3589–3594, Toulouse, France, July 2017.

14. S. Lucia, J.A. Paulson  , R. Findeisen, and R. D. Braatz. On stability of stochastic linear systems via polynomial chaos expansions. In Proc. of the American Control Conference , pages 5089–5094, Seattle, WA, May 2017.

13. E. Harinath, L. C. Foguth, J.A. Paulson  , and R. D. Braatz. Nonlinear model predictive control using polynomial optimization methods. In Proc. of the American Control Conference , pages 1–6, Boston, MA, July 2016.

12. E. Buehler, J.A. Paulson  , and A. Mesbah. Lyapunov-based stochastic nonlinear model predictive control: Shaping the state probability density functions. In Proc. of the American Control Conference , pages 5389–5394, Boston, MA, July 2016.

11. A. E. Lu, J.A. Paulson  , and R. D. Braatz. pH and conductivity control in an integrated biomanufacturing plant. In Proc. of the American Control Conference , pages 1741–1746, Boston, MA, July 2016.

10. T. Muehlpfordt, J.A. Paulson  , R. Findeisen, and R. D. Braatz. Output feedback model predictive control with probabilistic uncertainties for linear systems. In Proc. of the American Control Conference , pages 2035–2040, Boston, MA, July 2016.

9. J.A. Paulson  , M. C. Molaro, D. O. Bellisario, M. S. Strano, and R. D. Braatz. Mathematical modeling and analysis of carbon nanotube photovoltaic systems. In Proc. of the 11th IFAC Symposium on Dynamics and Control Process Systems , pages 442–447, Trondheim, Norway, June 2016.

8. J.A. Paulson  , E. Harinath, L. C. Foguth, and R. D. Braatz. Nonlinear model predictive control of systems with probabilistic time-invariant uncertainties. In Proc. of the 5th IFAC Conference on Nonlinear Model Predictive Control , pages 16–25, Seville, Spain, September 2015.

7. A. E. Lu, J.A. Paulson    (co-first author), N. J. Mozdzierz, A. Stockdale, A. N. Ford Versypt, K. R. Love, J. C. Love, and R. D. Braatz. Control systems technology in the advanced manufacturing of biologic drugs. In Proc. of the 2015 IEEE Conference on Control Applications , pages 1505–1515, Sydney, Australia, September 2015.

6. L. C. Foguth, J.A. Paulson   , R. D. Braatz, and D. M. Raimondo. Fast robust model predictive control of high-dimensional systems. In Proc. of the European Control Conference , pages 2009–2014, Linz, Austria, July 2015.

5. M. Torchio, N. A. Wolff, D. M. Raimondo, L. Magni, U. Krewer, B. Gopaluni, J.A. Paulson  , and R. D. Braatz. Real-time model predictive control for the optimal charging of a Lithium-ion battery. In Proc. of the American Control Conference , pages 4536–4541, Chicago, IL, July 2015.

4. A. Mesbah, J.A. Paulson  , R. Lakerveld, and R. D. Braatz. Plant-wide model predictive control for a continuous pharmaceutical process. In Proc. of the American Control Conference , pages 4301–4307, Chicago, IL, July 2015.

3.  J.A. Paulson   , S. Streif, and A. Mesbah. Stability for receding-horizon stochastic model predictive control with chance constraints. In Proc. of the American Control Conference , pages 937–943 Chicago, IL, July 2015.

2.  J.A. Paulson  , A. Mesbah, S. Streif, R. Findeisen, and R. D. Braatz. Fast stochastic model predictive control of high-dimensional systems. In Proc. of the 53rd IEEE Conference on Decision and Control , pages 2802–2809, Los Angeles, CA, December 2014.

1.  J.A. Paulson  , D. M. Raimondo, R. Findeisen, R. D. Braatz, and S. Streif. Guaranteed active fault diagnosis for uncertain nonlinear systems. In Proc. of the European Control Conference , pages 926–931, Strasbourg, France, June 2014.

21. J.A. Paulson, T. A. N. Heirung, and A. Mesbah. Tube-based robust nonlinear model predictive control with guaranteed fault tolerance. Submitted to Proc. of ACC.

20. J.A. Paulson  and A. Mesbah. Arbitrary polynomial chaos for quantification of general probabilistic uncertainties: Shaping closed-loop behavior of nonlinear systems. In Proc. of the IEEE Conference on Decision and Control, 2018 (accepted).

19. J.A. Paulson  and A. Mesbah. Nonlinear model predictive control with explicit backoffs for stochastic systems under arbitrary uncertainty. In Proc. of the IFAC Conference on Nonlinear Model Predictive Control, pages 622–633, Madison, WI, August 2018.

18. T. L. M. Santos, J.A. Paulson, and A. Mesbah. Offset-free stochastic model predictive control with enlarged feasibility region. In Proc. of the American Control Conference, pages 742–748, Milwaukee, WI June 2018.

17. J.A. Paulson, T. A. N. Heirung, R. D. Braatz, and A. Mesbah. Closed-loop active fault diagnosis for stochastic linear systems. In Proc. of the American Control Conference, pages 735–741, Milwaukee, WI June 2018.

16. J.A. Paulson, E. Buehler, and A. Mesbah. Arbitrary polynomial chaos for uncertainty propagation of correlated random variables in dynamic systems. In Proc. of the IFAC World Congress, pages 3607–3612, Toulouse, France, July 2017.

15. J.A. Paulson, L. Xie, and A. Mesbah. Offset-free robust MPC of systems with mixed stochastic and deterministic uncertainty. In Proc. of the IFAC World Congress, pages 3589–3594, Toulouse, France, July 2017.

14. S. Lucia, J.A. Paulson, R. Findeisen, and R. D. Braatz. On stability of stochastic linear systems via polynomial chaos expansions. In Proc. of the American Control Conference, pages 5089–5094, Seattle, WA, May 2017.

13. E. Harinath, L. C. Foguth, J.A. Paulson, and R. D. Braatz. Nonlinear model predictive control using polynomial optimization methods. In Proc. of the American Control Conference, pages 1–6, Boston, MA, July 2016.

12. E. Buehler, J.A. Paulson, and A. Mesbah. Lyapunov-based stochastic nonlinear model predictive control: Shaping the state probability density functions. In Proc. of the American Control Conference, pages 5389–5394, Boston, MA, July 2016.

11. A. E. Lu, J.A. Paulson, and R. D. Braatz. pH and conductivity control in an integrated biomanufacturing plant. In Proc. of the American Control Conference, pages 1741–1746, Boston, MA, July 2016.

10. T. Muehlpfordt, J.A. Paulson, R. Findeisen, and R. D. Braatz. Output feedback model predictive control with probabilistic uncertainties for linear systems. In Proc. of the American Control Conference, pages 2035–2040, Boston, MA, July 2016.

9. J.A. Paulson, M. C. Molaro, D. O. Bellisario, M. S. Strano, and R. D. Braatz. Mathematical modeling and analysis of carbon nanotube photovoltaic systems. In Proc. of the 11th IFAC Symposium on Dynamics and Control Process Systems, pages 442–447, Trondheim, Norway, June 2016.

8. J.A. Paulson, E. Harinath, L. C. Foguth, and R. D. Braatz. Nonlinear model predictive control of systems with probabilistic time-invariant uncertainties. In Proc. of the 5th IFAC Conference on Nonlinear Model Predictive Control, pages 16–25, Seville, Spain, September 2015.

7. A. E. Lu, J.A. Paulson (co-first author), N. J. Mozdzierz, A. Stockdale, A. N. Ford Versypt, K. R. Love, J. C. Love, and R. D. Braatz. Control systems technology in the advanced manufacturing of biologic drugs. In Proc. of the 2015 IEEE Conference on Control Applications, pages 1505–1515, Sydney, Australia, September 2015.

6. L. C. Foguth, J.A. Paulson, R. D. Braatz, and D. M. Raimondo. Fast robust model predictive control of high-dimensional systems. In Proc. of the European Control Conference, pages 2009–2014, Linz, Austria, July 2015.

5. M. Torchio, N. A. Wolff, D. M. Raimondo, L. Magni, U. Krewer, B. Gopaluni, J.A. Paulson, and R. D. Braatz. Real-time model predictive control for the optimal charging of a Lithium-ion battery. In Proc. of the American Control Conference, pages 4536–4541, Chicago, IL, July 2015.

4. A. Mesbah, J.A. Paulson, R. Lakerveld, and R. D. Braatz. Plant-wide model predictive control for a continuous pharmaceutical process. In Proc. of the American Control Conference, pages 4301–4307, Chicago, IL, July 2015.

3. J.A. Paulson, S. Streif, and A. Mesbah. Stability for receding-horizon stochastic model predictive control with chance constraints. In Proc. of the American Control Conference, pages 937–943 Chicago, IL, July 2015.

2. J.A. Paulson, A. Mesbah, S. Streif, R. Findeisen, and R. D. Braatz. Fast stochastic model predictive control of high-dimensional systems. In Proc. of the 53rd IEEE Conference on Decision and Control, pages 2802–2809, Los Angeles, CA, December 2014.

1. J.A. Paulson, D. M. Raimondo, R. Findeisen, R. D. Braatz, and S. Streif. Guaranteed active fault diagnosis for uncertain nonlinear systems. In Proc. of the European Control Conference, pages 926–931, Strasbourg, France, June 2014.

• Stochastic nonlinear model predictive control with probabilistic constraints. Identification and Control of Dynamic Systems Laboratory, University of Pavia , July 2014.
• Fast stochastic model predictive control of high-dimensional systems. Department of Chemical and Biomolecular Engineering, University of California, Berkeley , January 2015.
• Model predictive control of a continuous end-to-end pharmaceutical manufacturing pilot plant.  Process Systems Engineering Consortium, University of California, Santa Barbara , August 2015.
• Advanced control methods for complex chemical and biological systems. Department of Chemical and Life Science Engineering, Virginia Commonwealth University , January 2018.
• Advanced control methods for complex chemical and biological systems. Department of Chemical and Biomolecular Engineering, The Ohio State University , February 2018.
• Advanced control methods for complex chemical and biological systems. Department of Chemical Engineering, University of Texas at Austin , February 2018.
• Arbitrary polynomial chaos for uncertainty quantification of correlated random variables in nonlinear systems. AIChE Webinar Series-CAST , March 2018.
• Parameter estimation and model reduction. Center for Reproducible Biomedical Modeling, Online Seminar, June 2019.
• What happens when machine learning meets model predictive control? The University of British Columbia , February 2021.
• J.A. Paulson and A. Mesbah. The non-smooth polynomial chaos expansion (nsPCE) toolbox. University of California, Berkeley, July 17, 2019. https://github.com/joelpaulson/nsPCE
• J.A. Paulson and A. Mesbah. Data-driven scenario optimization for automated controller tuning with probabilistic performance guarantees. The Ohio State University, November 22, 2020. https://github.com/joelpaulson/LCSS_DataDrivenScenarioOptimization

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Theses and Dissertations

Hybrid machine learning and physics-based modeling approaches for process control and optimization.

Junho Park , Brigham Young University Follow

Transformer neural networks have made a significant impact on natural language processing. The Transformer network self-attention mechanism effectively addresses the vanishing gradient problem that limits a network learning capability, especially when the time series gets longer or the size of the network gets deeper. This dissertation examines the usage of the Transformer model for time-series forecasting and customizes it for a simultaneous multistep-ahead prediction model in a surrogate model predictive control (MPC) application. The proposed method demonstrates enhanced control performance and computation efficiency compared to the Long-short term memory (LSTM)-based MPC and one-step-ahead prediction model structures for both LSTM and Transformer networks. In addition to the Transformer, this research investigates hybrid machine-learning modeling. The machine learning models are known for superior function approximation capability with sufficient data. However, the quantity and quality of data to ensure the prediction precision are usually not readily available. The physics-informed neural network (PINN) is a type of hybrid modeling method using dynamic physics-based equations in training a standard machine learning model as a form of multi-objective optimization. The PINN approach with the state-of-the-art time-series neural networks Transformer is studied in this research providing the standard procedure to develop the Physics-Informed Transformer (PIT) and validating with various case studies. This research also investigates the benefit of nonlinear model-based control and estimation algorithms for managed pressure drilling (MPD). This work presents a new real-time high-fidelity flow model (RT-HFM) for bottom-hole pressure (BHP) regulation in MPD operations. Lastly, this paper presents details of an Arduino microcontroller temperature control lab as a benchmark for modeling and control methods. Standard benchmarks are essential for comparing competing models and control methods, especially when a new method is proposed. A physical benchmark considers real process characteristics such as the requirement to meet a cycle time, discrete sampling intervals, communication overhead with the process, and model mismatch. Novel contributions of this work are (1) a new MPC system built upon a Transformer time-series architecture, (2) a training method for time-series machine learning models that enables multistep-ahead prediction, (3) verification of Transformer MPC solution time performance improvement (15 times) over LSTM networks, (4) physics-informed machine learning to improve extrapolation potential, and (5) two case studies that demonstrate hybrid modeling and benchmark performance criteria.

College and Department

Ira A. Fulton College of Engineering and Technology; Chemical Engineering

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BYU ScholarsArchive Citation

Park, Junho, "Hybrid Machine Learning and Physics-Based Modeling Approaches for Process Control and Optimization" (2022). Theses and Dissertations . 9759. https://scholarsarchive.byu.edu/etd/9759

Date Submitted

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Dissertation

http://hdl.lib.byu.edu/1877/etd12597

transformer neural network architecture, physics informed neural network, process control, optimization

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