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 ...

Porous media play a critical role in various industrial fields due to their complex pore networks and considerable specific surface areas. The transport and reaction phenomena within porous media are ...