Emulating the evolution of phase separating microstructures using low-dimensional tensor decomposition and nonlinear regression
Emulating the evolution of phase separating microstructures using low-dimensional tensor decomposition and nonlinear regression
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DOI：
10.1557/s43577-022-00443-x
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发表时间：
2023-01
期刊：
影响因子：
5
通讯作者：
A. Iquebal;Peichen Wu;A. Sarfraz;K. Ankit
中科院分区：
文献类型：
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作者：
A. Iquebal;Peichen Wu;A. Sarfraz;K. Ankit
摘要相场法是一种有吸引力的计算工具，用于模拟相分离过程中的微观结构演变，包括凝固和旋节分解。然而，目前与求解相场方程相关的高计算成本限制了我们理解相变的能力。本文报道了一种新的相场仿真器的基础上张量分解的不断发展的微观结构和相应的两点相关函数，以预测微观结构的演变在任意小的时间尺度，否则不平凡的实现使用传统的相场方法。报告的技术是基于通过张量分解获得的低维表示的微观结构，随后，预测的微观结构的演变在低维空间中使用高斯过程回归（GPR）。一旦我们获得了在低维空间的微观结构预测，我们采用混合输入输出相位检索算法来重建的微观结构。作为概念的证明，我们提出了亚稳分解的微观结构预测的结果，虽然该方法本身是不可知的材料参数。结果表明，我们能够预测微观结构演化序列，非常类似于真实的微观结构（平均归一化均方为6.78 × 10 - 7）的时间尺度的一半，在获得训练数据。我们的数据驱动的微结构仿真器通过利用相场模拟和物理实验开辟了预测微结构演变的新途径，其中由于资源有限和物理约束，时间分辨率通常相当大，例如以前在微重力下进行的相粗化实验。相场法是一种有吸引力的计算工具，用于模拟相分离过程中的微观结构演变，包括凝固和旋节分解。然而，它们仍然是计算密集型的，由于严格限制的最大时间和长度尺度所施加的数值方法。本研究提出了一个相场仿真器，将预测相分离材料中观察到的微观结构的演变，利用现有的数据集从传统的相场建模方法。相场仿真器，这是第一次，耦合张量表示和非参数张量方法与微观结构建模和表示，将使高通量和易于预测的微观结构的演变，而不是解决计算密集型相场模拟每当一个新的模拟需要进行。我们的数据驱动的微结构仿真器通过利用相场模拟和物理实验开辟了预测微结构演变的新途径，其中由于资源有限和物理约束，时间分辨率通常相当大，例如以前在微重力下进行的相粗化实验。图形摘要
Abstract The phase-field method is an attractive computational tool for simulating microstructural evolution during phase separation, including solidification and spinodal decomposition. However, the high computational cost associated with solving phase-field equations currently limits our ability to comprehend phase transformations. This article reports a novel phase-field emulator based on the tensor decomposition of the evolving microstructures and their corresponding two-point correlation functions to predict microstructural evolution at arbitrarily small time scales that are otherwise nontrivial to achieve using traditional phase-field approaches. The reported technique is based on obtaining a low-dimensional representation of the microstructures via tensor decomposition, and subsequently, predicting the microstructure evolution in the low-dimensional space using Gaussian process regression (GPR). Once we obtain the microstructure prediction in the low-dimensional space, we employ a hybrid input–output phase-retrieval algorithm to reconstruct the microstructures. As proof of concept, we present the results on microstructure prediction for spinodal decomposition, although the method itself is agnostic of the material parameters. Results show that we are able to predict microstructure evolution sequences that closely resemble the true microstructures (average normalized mean square of $$6.78 \times 10^{-7}$$ 6.78 × 10 - 7 ) at time scales half of that employed in obtaining training data. Our data-driven microstructure emulator opens new avenues to predict the microstructural evolution by leveraging phase-field simulations and physical experimentation where the time resolution is often quite large due to limited resources and physical constraints, such as the phase coarsening experiments previously performed in microgravity. Impact statement The phase-field method is an attractive computational tool for simulating microstructural evolution during phase separation, including solidification and spinodal decomposition. However, they remain computationally intensive due to the strict limits on the maximum time and length scales imposed by the numerical methods. This research presents a phase-field emulator that will predict the microstructural evolution observed in phase separating materials by leveraging the already existing data sets obtained from traditional phase-field modeling approaches. The phase-field emulator, which for the first time, couples a tensor representation and nonparametric tensor methods with microstructure modeling and representation, will enable high-throughput and facile prediction of the microstructural evolution, as opposed to solving computationally intensive phase-field simulations whenever a new simulation needs to be performed. Our data-driven microstructure emulator opens new avenues to predict the microstructural evolution by leveraging phase-field simulations and physical experimentation where the time resolution is often quite large due to limited resources and physical constraints, such as the phase coarsening experiments previously performed in microgravity. Graphical Abstract