Waveguide-based structures can solve partial differential equations by mimicking elements in standard electronic circuits. This novel approach, developed by researchers at Newcastle University in the ...

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.

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 ...

By implementing AI to solve these equations, large-scale systems can be analyzed effectively in a fraction of the time it would take with traditional methods.

In this paper we shall prove the following theorem: Let K be a differential field of characteristic zero. Let φ and ψ be elements of a differential field extension of K such that (i) φ ≠ 0 and ψ ≠ 0; ...