基于 Cahn-Hilliard 流的物理启发神经网络在材料三维微观结构演化中的极端时间外推能力与热力学一致性
Extreme time extrapolation capabilities and thermodynamic consistency of physics-inspired Neural Networks for the 3D microstructure evolution of materials via Cahn-Hilliard flow
AI总结：
本研究训练了一种物理启发的卷积循环神经网络（CRNN），用于重现三维 Cahn-Hilliard 方程描述的调幅分解过程，在极低计算成本下实现了极长时间外推与热力学一致性，为材料高通量模拟提供了高准确性的新工具。
摘要：
一个卷积循环神经网络（CRNN）被训练用于重现 Cahn-Hilliard 方程所描述的三维调幅分解过程的演化。一种专门的物理启发架构被证明能够在预测演化与通过传统积分方案获得的真实演化之间提供高度的一致性。该方法能够以极低的计算成本准确重现训练集中未表示的微观结构演化。尽管训练集仅包含演化过程中相对短暂的初始阶段，但该方法实现了极长时间的外推能力，直至达到系统理论上预期的平衡状态，该状态由分层且相分离的形态组成。此外，在直至后期粗化阶段，也证明了与自由能衰减速率的定量一致性，证明了这类机器学习方法可以成为材料长时间尺度与高通量模拟的全新强大工具，同时保持热力学一致性与高准确性。
英文摘要：
A Convolutional Recurrent Neural Network (CRNN) is trained to reproduce the evolution of the spinodal decomposition process in three dimensions as described by the Cahn-Hilliard equation. A specialized, physics-inspired architecture is proven to provide close accordance between the predicted evolutions and the ground truth ones obtained via conventional integration schemes. The method can accurately reproduce the evolution of microstructures not represented in the training set at a fraction of the computational costs. Extremely long-time extrapolation capabilities are achieved, up to reaching the theoretically expected equilibrium state of the system, consisting of a layered, phase-separated morphology, despite the training set containing only relatively-short, initial phases of the evolution. Quantitative accordance with the decay rate of the Free energy is also demonstrated up to the late coarsening stages, proving that this class of Machine Learning approaches can become a new and powerful tool for the long timescale and high throughput simulation of materials, while retaining thermodynamic consistency and high-accuracy.
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