Theoretical and computational methods for scientific and engineering problems play major roles at Caltech. Dedicated contributors in related areas of ODE and PDE theory, numerical algorithms and analysis, high-performance computing and machine learning include Oscar Bruno, Thomas Hou, Houman Owhadi, Peter Schröder, Andrew Stuart. Specific applications include fluid-dynamics, solid mechanics, electromagnetism, spectral methods, multiple scale problems. Joel Tropp develops and analyzes algorithms for large-scale matrix computations and for optimization problems. Andrew Stuart is known for his work in the development of theory and algorithms for the solution of Bayesian inverse problems on function space. Tom Hou is known for his work in the development of multiscale finite element methods and for fluid interface problems.
Houman Owhadi has developed state of the art solvers for dense kernel matrices and elliptic operators. He is known for the introduction of data-adapted kernels and sparse approximation as methods for learning differential equations. Oscar Bruno specializes in the development of fast algorithms of high accuracy for general structures of interest in science and engineering, with applications concerning remote sensing, communications, photonics, antennas, and ground, air and space vehicles.