用物理约束神经网络预测相分离系统演化，精度高且长期稳定。
Physics-guided Convolutional Neural Network for Domain Growth Prediction in Systems with Conserved Kinetics
- 引入注意力机制与物理规律约束，构建守恒动力学系统的神经网络代理模型。
- 能准确预测临界与非临界混合物的长期相分离过程，保持组分守恒。
- 符合Lifshitz-Slyozov域生长定律，适合复杂动力系统建模研究者使用。
许多物理、化学和生物系统的时空演化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成本高昂的传统数值求解器的高效替代方案受到广泛关注。本文提出一种基于注意力机制的物理引导卷积神经网络，作为此类系统微观结构演化的代理模型。模型在二元混合物受Cahn-Hilliard方程控制的相分离过程中进行训练，可准确预测整个时间演化过程。结果显示，该代理模型在临界与非临界混合物上的长时间滚动预测均保持稳定与准确，并始终维持混合物组分守恒。此外，模型能精确捕捉域尺寸的增长，且与Lifshitz-Slyozov域生长定律一致。结果表明，该框架在建模守恒动力学系统方面具有显著有效性，可扩展至其他复杂动力系统。
原文摘要 · Abstract (English)
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. 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. 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. 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.
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