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 ...

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 ...

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 ...

The hype surrounding machine learning, a form of artificial intelligence, can make it seem like it is only a matter of time before such techniques are used to solve all scientific problems. While ...