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arXiv · 2506.01453

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

Igor Ciril·Khalil Haddaoui·Yohann Tendero
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Abstract

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.

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Igor Ciril, Khalil Haddaoui, Yohann Tendero. 2025-06-02. From Initial Data to Boundary Layers: Neural Networks for Nonlinear Hyperbolic Conservation Laws. https://arxiv.org/abs/2506.01453

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