L-MAU:通过低维方法预测卡恩-希利亚德微观结构演变的多变量时间序列网络

IF 7.2 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Sheng-Jer Chen, Hsiu-Yu Yu
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引用次数: 0

摘要

相场模型是预测各种相变过程的重要介观计算框架。机器学习算法的最新进展为通过数据驱动的降维技术加速模拟提供了可能。在此,我们详细介绍了我们开发的多变量时空预测网络(称为线性化运动感知单元(L-MAU)),该网络可精确预测尺寸缩小的相场微结构。我们采用包含 Flory-Huggins 自由能函数和浓度相关流动性的 Cahn-Hilliard 数值方程来生成训练和验证数据。这个全面的数据集涵盖了表现出液滴状和双连续模式的慢速和快速粗化系统。为了解决计算复杂性问题,我们提出了三种降维方法:(I) 两点相关函数(TPCF)与主成分分析(PCA);(II) 低压缩自动编码器(LCA)与 PCA;(III) 高压缩自动编码器(HCA)。在完成转换、预测和重建等步骤后,我们使用统计描述符(包括平均 TPCF、结构因子、域增长和结构相似性指数度量(SSIM))对结果进行了严格评估,以确保机器预测的准确性。对比分析表明,采用 300 个主成分的双阶段生命周期分析方法可以获得最佳结果,并具有准确的进化动态和重建形态。此外,将物理质量守恒约束纳入这种双阶段配置(称为 C-LCA)可产生更一致、更紧凑的低维表示,从而进一步增强时空特征预测。这种新颖的降维方法可以在误差可控的情况下对相场演变进行高保真预测,最终恢复的微观结构可以稳健地改进数值积分,以实现所需的后期相分离形态。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
L-MAU: A multivariate time-series network for predicting the Cahn-Hilliard microstructure evolutions via low-dimensional approaches

The phase-field model is a prominent mesoscopic computational framework for predicting diverse phase change processes. Recent advancements in machine learning algorithms offer the potential to accelerate simulations by data-driven dimensionality reduction techniques. Here, we detail our development of a multivariate spatiotemporal predicting network, termed the linearized Motion-Aware Unit (L-MAU), to predict phase-field microstructures at reduced dimensions precisely. We employ the numerical Cahn-Hilliard equation incorporating the Flory-Huggins free energy function and concentration-dependent mobility to generate training and validation data. This comprehensive dataset encompasses slow- and fast-coarsening systems exhibiting droplet-like and bicontinuous patterns. To address computational complexity, we propose three dimensionality reduction pipelines: (I) two-point correlation function (TPCF) with principal component analysis (PCA), (II) low-compression autoencoder (LCA) with PCA, and (III) high-compression autoencoder (HCA). Following the steps of transformation, prediction, and reconstruction, we rigorously evaluate the results using statistical descriptors, including the average TPCF, structure factor, domain growth, and the structural similarity index measure (SSIM), to ensure the fidelity of machine predictions. A comparative analysis reveals that the dual-stage LCA approach with 300 principal components delivers optimal outcomes with accurate evolution dynamics and reconstructed morphologies. Moreover, incorporating the physical mass-conservation constraint into this dual-stage configuration (designated as C-LCA) produces more coherent and compact low-dimensional representations, further enhancing spatiotemporal feature predictions. This novel dimensionality reduction approach enables high-fidelity predictions of phase-field evolutions with controllable errors, and the final recovered microstructures may improve numerical integration robustly to achieve desired later-stage phase separation morphologies.

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来源期刊
Computer Physics Communications
Computer Physics Communications 物理-计算机:跨学科应用
CiteScore
12.10
自引率
3.20%
发文量
287
审稿时长
5.3 months
期刊介绍: The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper. Computer Programs in Physics (CPiP) These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged. Computational Physics Papers (CP) These are research papers in, but are not limited to, the following themes across computational physics and related disciplines. mathematical and numerical methods and algorithms; computational models including those associated with the design, control and analysis of experiments; and algebraic computation. Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.
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