Efficient Weak-Entropy PINN for Solving Hyperbolic Conservation Laws
In recent years, neural networks have significantly advanced numerical solutions of partial differential equations (PDEs). However, solving PDEs with discontinuous solutions, such as hyperbolic conservation laws, remains challenging for neural network-based methods such as physics-informed neural networks (PINNs). Existing methods often rely on strong prior assumptions such as knowledge of discontinuity locations, or they introduce artificial smoothing terms that degrade accuracy. However, accurately solving these conservation laws and predicting the formation and propagation of discontinuities in solutions is crucial in many practical applications, including gas dynamics and traffic flow...
| Authors | Qi Gao, Kuang Huang, Xuan Di |
|---|---|
| Primary category | math.NA |
| Published | 11 August 2026 |
| Last updated at source | 11 August 2026 |
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