From Initial Data to Boundary Layers: Neural Networks for Nonlinear Hyperbolic Conservation Laws
This work addresses a domain-specific problem in computational physics and engineering, with potential applications to industrial scenarios, but it appears incremental as it builds on existing methods for hyperbolic conservation laws.
The paper tackles approximating entropy solutions for nonlinear hyperbolic conservation laws using neural networks, introducing a framework that achieves fast convergence and accurate predictions in one-dimensional scalar test cases.
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.