Adversarial Sampling for Solving Differential Equations with Neural Networks
Abstract
Neural network-based methods for solving differential equations have been gaining traction. They work by improving the differential equation residuals of a neural network on a sample of points in each iteration. However, most of them employ standard sampling schemes like uniform or perturbing equally spaced points. We present a novel sampling scheme which samples points adversarially to maximize the loss of the current solution estimate. A sampler architecture is described along with the loss terms used for training. Finally, we demonstrate that this scheme outperforms pre-existing schemes by comparing both on a number of problems.
Cite
Text
Parwani and Protopapas. "Adversarial Sampling for Solving Differential Equations with Neural Networks." NeurIPS 2021 Workshops: DLDE, 2021.Markdown
[Parwani and Protopapas. "Adversarial Sampling for Solving Differential Equations with Neural Networks." NeurIPS 2021 Workshops: DLDE, 2021.](https://mlanthology.org/neuripsw/2021/parwani2021neuripsw-adversarial/)BibTeX
@inproceedings{parwani2021neuripsw-adversarial,
title = {{Adversarial Sampling for Solving Differential Equations with Neural Networks}},
author = {Parwani, Kshitij and Protopapas, Pavlos},
booktitle = {NeurIPS 2021 Workshops: DLDE},
year = {2021},
url = {https://mlanthology.org/neuripsw/2021/parwani2021neuripsw-adversarial/}
}