Score-Based Stabilization for Time-Dependent Problems

• URL: http://arxiv.org/abs/2607.25119v1
• Date: Mon, 27 Jul 2026 22:26:54 GMT
• Title: Score-Based Stabilization for Time-Dependent Problems
• Abstract summary: We propose a score-based stabilization framework for numerical simulation of partial differential equations.<n>We show that the stabilization operator acts as a contraction toward this manifold, yielding a correction mechanism with basin-conditional stability.
• Score: 5.288977149942441
• License: http://creativecommons.org/licenses/by/4.0/
• 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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