Department of Mathematics

Many dynamical systems in science and engineering are described by mathematical models, often formulated as systems of ordinary or partial differential equations. These models, however, are only appro... More

Computing high-dimensional partial differential equations (PDEs) remains an important yet challenging problem in computational mathematics. In this work, we propose a scalable deep learning–based al... More

Three Ph.D. candidates defending this semester will present previews of their defenses.

Unmanned underwater vehicles (UUV) integrate ocean forecasts with path planning algorithms to identify energy- or time-minimizing paths that allow for task completion.  A crucial account in determini... More

In this talk, we will discuss the construction of the 2D Finite Element solver for Poisson\'s equation. This FEM solver will use triangular mesh generation, reference-to-physical mappings, triangleMore

The classification of topological phases of matter has traditionally relied on assumptions about the underlying material, requiring that the material be an insulator with a well-defined band structure... More

Neural operators such as DeepONet and Fourier Neural Operators have shown remarkable promise in learning solution mappings for parametric partial differential equations, offering orders-of-magnitude s... More