Machine-learning-based spectral methods for partial differential equations.

ABSTRACT: Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the solution of a PDE. The last decade has seen the emergence of deep learning as a strong contender in providing efficient representations of complex functions. In the current work, we present an approach for combining deep neural networks with spectral methods to solve PDEs. In particular, we use a deep learning technique known as the Deep Operator Network (DeepONet) to identify candidate functions on which to expand the solution of PDEs. We have devised an approach that uses the candidate functions provided by the DeepONet as a starting point to construct

SUBMITTER: Meuris B 

PROVIDER: S-EPMC9889394 | biostudies-literature | 2023 Jan

REPOSITORIES: biostudies-literature