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 ...

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 ...

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.

We were always taught that the fundamental passive components were resistors, capacitors, and inductors. But in 1971, [Leon Chua] introduced the idea of a memristor — a sort of resistor with memory.

Mathematicians finally understand the behavior of an important class of differential equations that describe everything from ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...