HypNO: A Graph-Based Neural Operator with Physics-Informed Message Passing for Hyperbolic Conservation Laws
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Abstract (arXiv)
We introduce HypNO, a graph-based neural operator for scalar hyperbolic conservation laws. HypNO operates directly on a space-time graph of finite-volume cells and uses adjacency-factored, physics-informed message passing to respect upwinding and entropy admissibility near shocks. We benchmark the architecture on the Lighthill-Whitham-Richards (LWR) and Aw-Rascle-Zhang (ARZ) traffic-flow models, a stress test for operator-learning methods because of their simultaneous global transport and shock formation. HypNO predicts solution snapshots accurately across a range of initial conditions while capturing the shocks and discontinuities of the solution.
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References · 5
- 2016Gaussian Error Linear Units (GELUs)cited by 3,502
- 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 349
- 2019Variational Physics-Informed Neural Networks For Solving Partial Differential Equationscited by 148
- 2024Approximating Numerical Fluxes Using Fourier Neural Operators for Hyperbolic Conservation Lawscited by 11
- 2026Supervised and Unsupervised Neural Network Solver for First Order Hyperbolic Nonlinear PDEscited by 1
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