mlsanityData to 14 Oct 2026

SPIKE: Stable Physics-Informed Kernel Evolution Method for Solving Hyperbolic Conservation Laws

arXiv 2510.18266 ↗First posted 21 Oct 2025math.NA cs.AI cs.LGcited by 1

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Abstract (arXiv)

We introduce the Stable Physics-Informed Kernel Evolution (SPIKE) method for numerical computation of inviscid hyperbolic conservation laws. SPIKE resolves a fundamental paradox: how strong-form residual minimization can capture weak solutions containing discontinuities. SPIKE employs reproducing kernel representations with regularized parameter evolution, where Tikhonov regularization provides a smooth transition mechanism through shock formation, allowing the dynamics to traverse shock singularities. This approach automatically maintains conservation, tracks characteristics, and captures shocks satisfying Rankine-Hugoniot conditions within a unified framework requiring no explicit shock detection or artificial viscosity. Numerical validation across scalar and vector-valued conservation laws confirms the method's effectiveness.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 13 of its 46 references that are in the map. First posted on arXiv 21 Oct 2025.

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13 of 46 references.

References · 13

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1 more
  1. 2025Regularized dynamical parametric approximation of stiff evolution problemscited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Efficient Weak-Entropy PINN for Solving Hyperbolic Conservation Lawscited by 0