Physics-guided Convolutional Neural Network for Domain Growth Prediction in Systems with Conserved Kinetics

基于物理引导卷积神经网络的守恒动力学系统畴增长预测

Abstract: The spatiotemporal evolution of many physical, chemical, and biological systems is described by nonlinear partial differential equations (PDEs). Recently, deep neural network-based surrogate models have gained increasing interest as efficient alternatives to computationally expensive traditional numerical solvers. 摘要： 许多物理、化学和生物系统的时空演化通常由非线性偏微分方程（PDEs）描述。近年来，基于深度神经网络的代理模型作为计算昂贵的传统数值求解器的高效替代方案，受到了越来越多的关注。

In this work, we propose an attention-based, physics-guided convolutional neural network as a surrogate model to learn the microstructural evolution of such systems. We train the model to accurately predict the full time-evolution of phase separation in binary mixtures governed by the Cahn-Hilliard equation. 在这项工作中，我们提出了一种基于注意力机制的物理引导卷积神经网络，作为学习此类系统微观结构演化的代理模型。我们训练该模型，以准确预测受 Cahn-Hilliard 方程控制的二元混合物中相分离的完整时间演化过程。

We show that predictions from our trained surrogate model remain stable and accurate over long-time rollouts for both critical and off-critical mixtures and preserve the mixture composition throughout evolution. We also show that our model accurately captures the growth of domain size and is consistent with the Lifshitz-Slyozov domain-growth law. 研究表明，我们训练的代理模型在临界和非临界混合物的长期演化预测中均保持稳定且准确，并在整个演化过程中保持了混合物成分的守恒。我们还证明了该模型能够准确捕捉畴尺寸的增长，并符合 Lifshitz-Slyozov 畴增长定律。

The prediction results demonstrate the effectiveness of the proposed framework for modeling systems with conserved kinetics and can be extended to other complex dynamical systems. 预测结果证明了所提框架在模拟具有守恒动力学系统方面的有效性，并可扩展至其他复杂的动力系统。

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Paper Details:

• Authors: Vijay Yadav, Madhu Priya, Manish Dev Shrimali, Prabhat K. Jaiswal
• arXiv ID: 2606.26128
• Subjects: Machine Learning (cs.LG); Soft Condensed Matter (cond-mat.soft)

论文详情：

• 作者： Vijay Yadav, Madhu Priya, Manish Dev Shrimali, Prabhat K. Jaiswal
• arXiv ID: 2606.26128
• 学科分类： 机器学习 (cs.LG)；软凝聚态物理 (cond-mat.soft)