相场方法是一种流行的介观尺度计算方法，用于研究微结构及其物理性质的时空演化。它已被广泛用于描述各种重要的介观尺度演化现象，包括晶粒生长和粗化、凝固、薄膜沉积、位错动力学、生物膜中的囊泡形成和裂纹传播。现有的高保真相场模型实际计算成本很高，因为它们需要解决一组描述这些过程的连续场变量的耦合偏微分方程系统。目前，最大限度地降低计算成本的探索主要集中在利用高性能计算架构和先进的数值方案，或将机器学习算法与微观结构模拟相结合。然而，对于这些成功的解决方案来说，如何平衡精度与计算效率也还是个令人头痛的问题。要么计算效率高就不能保证得到精确解；要么可以求解复杂的、耦合的相场方程，却计算成本高昂；要么能够预测训练范围之内的微观结构演化，却预测不了训练之外的演化。
来自美国桑迪亚国家实验室集成纳米技术中心的Rémi Dingreville教授领导的团队，开发了一个机器学习框架来高效、快速地预测复杂的微结构演化问题。通过采用长短期记忆(LSTM)神经网络学习长期模式和解决历史依赖性问题，作者将微结构演化问题重新表述为多变量时间序列问题。在这种情况下，神经网络能学习如何通过微结构随时间演化的低维描述来预测微结构的演化。他们发现这种机器学习的替代模型，可以在几分之一秒的时间内预测两相混合物在亚稳态分解时的非线性微观结构演化，与高保真相场模拟相比，准确性仅损失5%。作者表明，该替代模型轨迹作为经典高保真相场模型的输入数据时，可以加速相场模拟。作者的解决方案开辟了一条很有前途的道路，在尺度现象至关重要的问题中（如材料设计等演化问题），可利用他们加速的相场模拟来发现、求解和预测加工-微结构-性能关系。该文近期发表于npj Computational Materials 7: 3 (2021)，英文标题与摘要如下，点击左下角“阅读原文”可以自由获取论文PDF。
Accelerating phase-field-based microstructure evolution predictions via surrogate models trained by machine learning methods
David Montes de Oca Zapiain, James A. Stewart & Rémi Dingreville
The phase-field method is a powerful and versatile computational approach for modeling the evolution of microstructures and associated properties for a wide variety of physical, chemical, and biological systems. However, existing high-fidelity phase-field models are inherently computationally expensive, requiring high-performance computing resources and sophisticated numerical integration schemes to achieve a useful degree of accuracy. In this paper, we present a computationally inexpensive, accurate, data-driven surrogate model that directly learns the microstructural evolution of targeted systems by combining phase-field and history-dependent machine-learning techniques. We integrate a statistically representative, low-dimensional description of the microstructure, obtained directly from phase-field simulations, with either a time-series multivariate adaptive regression splines autoregressive algorithm or a long short-term memory neural network. The neural-network-trained surrogate model shows the best performance and accurately predicts the nonlinear microstructure evolution of a two-phase mixture during spinodal decomposition in seconds, without the need for “on-the-fly” solutions of the phase-field equations of motion. We also show that the predictions from our machine-learned surrogate model can be fed directly as an input into a classical high-fidelity phase-field model in order to accelerate the high-fidelity phase-field simulations by leaping in time. Such machine-learned phase-field framework opens a promising path forward to use accelerated phase-field simulations for discovering, understanding, and predicting processing–microstructure–performance relationships.
