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arXiv · 2607.25119

Score-Based Stabilization for Time-Dependent Problems

Eshed Gal·Eldad Haber·Uri Ascher
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Abstract

We propose a score-based stabilization framework for numerical simulation of partial differential equations, in which a learned score model defines a stabilization operator applied to provisional numerical updates. This operator augments standard time-stepping schemes by enforcing structure and physical consistency through a correction that drives iterates toward the manifold of admissible states. We show that the stabilization operator acts as a contraction toward this manifold, yielding a correction mechanism with basin-conditional stability. Numerical experiments on Advection, Korteweg-de Vries (KdV), Nonlinear Schrodinger (NLS), and Burgers' equations demonstrate improved robustness, suppression of nonphysical instabilities, and preservation of qualitative dynamics.

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Eshed Gal, Eldad Haber, Uri Ascher. 2026-07-27. Score-Based Stabilization for Time-Dependent Problems. https://arxiv.org/abs/2607.25119

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