🤖 AI Summary
本文提出了一种物理约束的深度神经网络模型，用于预测二元混合物中的相分离演化，通过直接在输出上施加守恒约束，实现了长时间稳定和准确预测。
📝 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. 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.