Abstract: There has been significant recent work on solving PDEs using neural networks on infinite dimensional spaces. In this talk we consider two examples. First, we prove that transformers can ...

In the fields of physics, mathematics, and engineering, partial differential equations (PDEs) are essential for modeling various phenomena, from heat diffusion to particle motion and wave propagation.

Under the hood, multiphysics software based on the finite-element (FE) method mathematically models complex engineering and scientific problems in inductive heating, heat transfer, and ...

Luis Caffarelli has won the 2023 Abel prize, unofficially called the Nobel prize for mathematics, for his work on a class of equations that describe many real-world physical systems, from melting ice ...