A PINNs approach for the computation of eigenvalues in elliptic problems

TL;DR

This paper introduces a deep learning-based method for computing eigenvalues of elliptic problems that is dimension-independent, capable of finding any eigenvalue without prior calculations, and adaptable to nonlinear cases.

Contribution

The proposed PINNs approach is novel in its ability to compute eigenvalues independently of space dimension and handle nonlinear problems without prior eigenvalue computations.

Findings

Method successfully computes eigenvalues across various dimensions.

Approach can target arbitrary eigenvalues without sequential calculations.

Adaptable to nonlinear eigenvalue problems.

Abstract

In this paper, we propose a method for computing eigenvalues of elliptic problems using Deep Learning techniques. A key feature of our approach is that it is independent of the space dimension and can compute arbitrary eigenvalues without requiring the prior computation of lower ones. Moreover, the method can be easily adapted to handle nonlinear eigenvalue problems.