Neural Network-Assisted Refinement of Traditional Schemes for One-Dimensional Scalar Conservation Laws

arXiv:2609.32887 · math.NA, cs.LG, cs.NA · Submitted 2026-09-26 · Read on arXiv

math.NA, cs.LG, cs.NA

Submitted: 2026-09-26

Updated: 2026-09-26

Terminology

• Conservation Laws — 20× in this paper · explained in 3 episodes
• Initial Data — 17× in this paper · explained in 2 episodes
• Accuracy — 4× in this paper · explained in 1 episode
• Loss Function — 4× in this paper · explained in 2 episodes
• Core — 3× in this paper · explained in 2 episodes
• Activation Function — 2× in this paper · explained in 1 episode
• Adam — 1× in this paper · explained in 2 episodes
• Axioms — 1× in this paper · explained in 2 episodes
• DeepONet — 1× in this paper · explained in 2 episodes
• Inverse Problem — 1× in this paper · explained in 2 episodes
• Physics-Informed Neural Networks (PINNs) — 1× in this paper · explained in 6 episodes
• Robustness — 1× in this paper · explained in 5 episodes

Sources

• Designing Neural Networks for Hyperbolic Conservation Laws
• Entropy stable conservative flux form neural networks

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