Computational Mathematics and Analysis
The AMS computational mathematics group encompasses the pipeline of approximations spanning the more theoretical aspects through to efficient computation. This includes techniques for the solution to deterministic/stochastic partial differential equations (PDEs) that arise in mathematical biology, control theory, fluid dynamics, uncertainty qualification, as well as techniques useful in visualization and computer-aided geometric design. Emerging areas in the department include mean field games, optimization, and deep learning.
- Meshfree Approximation Methods
- Radial Basis Functions
- Approximation Theory
- Numerical Solution of PDEs
- Spline Theory
- Computer-Aided Geometric Design
- Stochastic, model reduction and multiscale algorithms
- Quantification of uncertainties in parallel scientific computing models
- Free surface nonlinear evolutionary systems with applications.
- Constructive approximations on spherical surfaces.
- Fully discrete spectral boundary integral and boundary element methods.
- Parallel evolutionary computations and analysis.
- Radial basis functions based numerical schemes for PDEs
- Zeroth-order optimization and applications
- Signal processing, particularly compressed sensing
- Learning-to-optimize for inverse problems
- Nonlinear dimensionality reduction
- First passage percolation
Brownian dynamics, Numerical methods for SDEs, Colloidal suspensions
Computational fluid dynamics, Immersed boundary methods
Simulating actin suspensions/fiber networks
Samy Wu Fung
- Inverse Problems, Optimization, Deep Learning
- Optimal Control, Mean Field Games