Doctoral Programs in Computational Science and Engineering

Computational Science and Engineering

Doctor of Philosophy in Computational Science and Engineering

Program Requirements

Core Subjects
18.335[J]Introduction to Numerical Methods12
CSE.900Doctoral Seminar in Computational Science and Engineering3
Core Area of Study
Choose four 12-unit subjects from these six core CSE areas: 148
Discretization and numerical methods for partial differential equations
Optimization methods
Statistics and data-driven modeling
High-performance computing and/or algorithms
Mathematical foundations (e.g., functional analysis, probability)
Modeling (i.e., a subject that treats mathematical modeling in any science or engineering discipline)
Computational Concentration 124
Unrestricted Electives24
Choose 24 units of additional graduate-level subjects in any field.
Thesis Research168-288
Total Units279-399

A program of study comprising subjects in the selected core areas and the computational concentration must be developed in consultation with the student’s doctoral thesis committee and approved by the CCSE graduate officer.

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

Computational Science and Engineering

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:

  • Aeronautics and Astronautics
    • Aerospace Engineering and Computational Science
    • Computational Science and Engineering (available only to students who matriculate in 2023–2024 or earlier)
  • Chemical Engineering
    • Chemical Engineering and Computation
  • Civil and Environmental Engineering
    • Civil Engineering and Computation
    • Environmental Engineering and Computation
  • Materials Science and Engineering
    • Computational Materials Science and Engineering
  • Mechanical Engineering
    • Mechanical Engineering and Computation
  • Nuclear Science and Engineering
    • Computational Nuclear Science and Engineering
    • Nuclear Engineering and Computation
  • Earth, Atmospheric and Planetary Sciences
    • Computational Earth, Science and Planetary Sciences
  • Mathematics
    • Mathematics and Computational Science

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

1.125Architecting and Engineering Software Systems12
1.545Atomistic Modeling and Simulation of Materials and Structures12
1.583Topology Optimization of Structures12
1.723Computational Methods for Flow in Porous Media12
2.098Introduction to Finite Element Methods12
2.156Artificial Intelligence and Machine Learning for Engineering Design12
2.168Learning Machines12
2.29Numerical Fluid Mechanics12
3.320Atomistic Computer Modeling of Materials12
4.450[J]Computational Structural Design and Optimization
6.7210[J]Introduction to Mathematical Programming12
6.7220[J]Nonlinear Optimization12
6.7230[J]Algebraic Techniques and Semidefinite Optimization12
6.7250Optimization for Machine Learning12
6.7300[J]Introduction to Modeling and Simulation12
6.7810Algorithms for Inference12
6.7830Bayesian Modeling and Inference12
6.7900Machine Learning 112
6.7940Dynamic Programming and Reinforcement Learning12
6.8300Advances in Computer Vision12
6.8410Shape Analysis12
6.C51Modeling with Machine Learning: from Algorithms to Applications 26
9.520[J]Statistical Learning Theory and Applications12
9.660Computational Cognitive Science12
10.551Systems Engineering 39
10.552Modern Control Design 39
10.554[J]Process Data Analytics12
10.557Mixed-integer and Nonconvex Optimization12
10.637[J]Computational Chemistry12
12.515Data and Models12
12.521Computational Geophysical Modeling12
12.620[J]Classical Mechanics: A Computational Approach12
12.714Computational Data Analysis12
12.805Data Analysis in Physical Oceanography12
12.850Computational Ocean Modeling12
15.070[J]Discrete Probability and Stochastic Processes12
15.077[J]Statistical Machine Learning and Data Science 112
15.083Integer Optimization12
15.093[J]Optimization Methods12
15.764[J]The Theory of Operations Management12
16.110Flight Vehicle Aerodynamics12
16.225[J]Computational Mechanics of Materials12
16.413[J]Principles of Autonomy and Decision Making12
16.888[J]Multidisciplinary Design Optimization12
16.920[J]Numerical Methods for Partial Differential Equations12
16.930Advanced Topics in Numerical Methods for Partial Differential Equations12
16.940Numerical Methods for Stochastic Modeling and Inference12
18.335[J]Introduction to Numerical Methods12
18.336[J]Fast Methods for Partial Differential and Integral Equations12
18.337[J]Parallel Computing and Scientific Machine Learning12
18.338Eigenvalues of Random Matrices12
18.369[J]Mathematical Methods in Nanophotonics12
18.435[J]Quantum Computation12
22.15Essential Numerical Methods6
22.212Nuclear Reactor Analysis II12
22.213Nuclear Reactor Physics III12
22.315Applied Computational Fluid Dynamics and Heat Transfer12
CSE.999Experiential Learning in Computational Science and Engineering
IDS.131[J]Statistics, Computation and Applications12

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


Credit can only be given for one of 6.7900, 15.077, or IDS.147.


Students cannot receive credit without simultaneous completion of a 6-unit Common Ground disciplinary module. The two subjects together count as one 12-unit subject. See 6.C51 for more information.


Students can receive credit for either 10.551 or 10.552 as a CSE concentration subject, but not both.


Subject to Sloan bidding process.