# From Initial Data to Boundary Layers: Neural Networks for Nonlinear Hyperbolic Conservation Laws

arXiv: https://arxiv.org/abs/2506.01453 · HTML: https://mlsanity.com/paper/2506.01453/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 16 references that are in the map.
- First posted on arXiv 2 Jun 2025.

## Builds on (most cited first, 1 of 1)

- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)

## Abstract (arXiv)

We address the approximation of entropy solutions to initial-boundary value problems for nonlinear strictly hyperbolic conservation laws using neural networks. A general and systematic framework is introduced for the design of efficient and reliable learning algorithms, combining fast convergence during training with accurate predictions. The methodology that relies on solving a certain relaxed related problem is assessed through a series of one-dimensional scalar test cases. These numerical experiments demonstrate the potential of the methodology developed in this paper and its applicability to more complex industrial scenarios.