Machine Learning for semi linear PDEs

TL;DR

This paper compares various neural network-based algorithms for solving semi-linear PDEs, introducing a new deep learning method that solves a fixed point problem and demonstrating its competitive accuracy.

Contribution

The paper presents a novel deep learning algorithm for semi-linear PDEs that solves a fixed point problem, showing competitive performance against existing methods.

Findings

The new algorithm achieves accuracy comparable to state-of-the-art methods.

Different neural network architectures and parameterizations are evaluated.

The fixed point approach offers a promising alternative for solving semi-linear PDEs.

Abstract

Recent machine learning algorithms dedicated to solving semi-linear PDEs are improved by using different neural network architectures and different parameterizations. These algorithms are compared to a new one that solves a fixed point problem by using deep learning techniques. This new algorithm appears to be competitive in terms of accuracy with the best existing algorithms.