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.
@article{arxiv.1809.07609,
title = {Machine Learning for semi linear PDEs},
author = {Quentin Chan-Wai-Nam and Joseph Mikael and Xavier Warin},
journal= {arXiv preprint arXiv:1809.07609},
year = {2018}
}