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arXiv · 2610.08088

A SAV Neural Network Method for Allen--Cahn and Cahn--Hilliard Equations

Tao Luo·Guihong Wang·Wei Zhao
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Abstract

Phase-field equations are fundamental examples of gradient-flow systems and require numerical solvers that preserve intrinsic energy dissipation. In this work, we propose a neural network-based method that combines an SAV time discretization with a mesh-free neural representation. We establish the unconditional energy stability of the underlying SAV semi-discretization, quantify the energy defect caused by solver residuals, and derive a conditional high-probability error estimate for the Allen--Cahn equation. Numerical experiments show that our approach consistently exhibits energy-stable behavior, while outperforming existing neural network-based solvers.

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Tao Luo, Guihong Wang, Wei Zhao. 2026-10-06. A SAV Neural Network Method for Allen--Cahn and Cahn--Hilliard Equations. https://arxiv.org/abs/2610.08088

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