A scalable framework for learning the geometry-dependent solution operators of partial differential equations.

ABSTRACT: Solving partial differential equations (PDEs) using numerical methods is a ubiquitous task in engineering and medicine. However, the computational costs can be prohibitively high when many-query evaluations of PDE solutions on multiple geometries are needed. Here we aim to address this challenge by introducing Diffeomorphic Mapping Operator Learning (DIMON), a generic artificial intelligence framework that learns geometry-dependent solution operators of different types of PDE on a variety of geometries. We present several examples to demonstrate the performance, efficiency and scalability of the framework in learning both static and time-dependent PDEs on parameterized and non-parameterized domains; these include solving the Laplace equations, reaction-diffusion equations and a system of m

SUBMITTER: Yin M 

PROVIDER: S-EPMC11659174 | biostudies-literature | 2024 Dec

REPOSITORIES: biostudies-literature