Computational Science & Numerical Analysis

Computational science is a key area related to physical mathematics. The problems of interest in physical mathematics often require computations for their resolution. Conversely, the development of efficient computational algorithms often requires an understanding of the basic properties of the solutions to the equations to be solved numerically. For example, the development of methods for the solution of hyperbolic equations (e.g. shock capturing methods in, say, gas-dynamics) has been characterized by a very close interaction between theoretical, computational, experimental scientists, and engineers.

Department Members in This Field

Faculty

• Laurent Demanet Applied analysis, Scientific Computing
• Alan Edelman Scientific Computing, Numerical Linear Algebra, Random Matrices
• Steven Johnson Waves, PDEs, Scientific Computing
• Pablo Parrilo Optimization, Control Theory, Computational Algebraic Geometry, Applied Mathematics
• Gilbert Strang Numerical Analysis, Partial Differential Equations
• John Urschel Matrix Analysis, Matrix Computations, Spectral Graph Theory

Instructors & Postdocs

• Joseph Berleant Representation theory, Geometric algebra
• Pengning Chao Scientific computing, Nanophotonics, Inverse problems, Fundamental limits
• Shi Chen Machine Learning, Gradient Flows and Optimization, Inverse Problems
• Ziang Chen applied analysis, applied probability, statistics, optimization, machine learning
• Nicholas Nelsen Scientific Machine Learning, Statistics, Inverse Problems

Researchers & Visitors

• Keaton Burns PDEs, Spectral Methods, Fluid Dynamics
• Raphaël Pestourie Surrogate Models; ML-enhanced Optimization; Optical Computing.

Graduate Students*

• Rodrigo Arrieta Candia Numerical methods for PDEs, Numerical Analysis, Scientific Computing, Computational Electromagnetism
• Diego Chavez Physical Applied Math, Waves
• Mo Chen Optimization, Scientific Computing
• Charlie Cowen-Breen PDE, machine learning, computer-assisted proofs
• Max Daniels High-dimensional statistics, optimization, sampling algorithms, machine learning
• Sarah Greer Imaging, inverse problems, signal processing
• Joonsoo Lee Applied Probability, Optimization
• Evelyne Ringoot High-Performance Computing
• Sarah Snider Physical Applied Mathematics, Computational Fluid Dynamics
• Songchen Tan computational science, numerical analysis, differentiable programming

*Only a partial list of graduate students