Partial differential equations (PDEs) are a class of mathematical problems that represent the interplay of multiple variables, and therefore have predictive power when it comes to complex physical ...

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 ...

The researchers’ device applies principles of neural networking to an optical framework. As a wave encoded with a PDE passes through the ONE’s series of components, its properties gradually shift and ...

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 ...

Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...