O. V. Kapustyan, I. I. Korol, O. N. Nesterenko, V. O. Skrynyk

Deep Neural Network Approach for Parabolic PDEs with Nonsmooth Interaction Functions

abstract:
In this paper, we propose a theoretical framework for approximating mild solutions of parabolic partial differential equations (PDEs) with nonsmooth interaction functions using deep neural networks.

Mathematics Subject Classification: 35A01, 35K58, 65M50

Key words and phrases: Semilinear parabolic equation, mild solutions, Galerkin method, deep neural networks