# Adversarial Sampling for Solving Differential Equations with Neural Networks

arXiv: https://arxiv.org/abs/2111.12024 · HTML: https://mlsanity.com/paper/2111.12024/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 10 references that are in the map.
- First posted on arXiv 20 Nov 2021.

## Builds on (most cited first, 4 of 4)

- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Solving Differential Equations Using Neural Network Solution Bundles](https://mlsanity.com/paper/2006.14372/) (2020)
- [Unsupervised Neural Networks for Quantum Eigenvalue Problems](https://mlsanity.com/paper/2010.05075/) (2020)

## Abstract (arXiv)

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.