{"title":"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","authors":"","doi":"10.1016/j.cpc.2024.109342","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":null,"pages":null},"PeriodicalIF":7.2000,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"L-MAU: A multivariate time-series network for predicting the Cahn-Hilliard microstructure evolutions via low-dimensional approaches\",\"authors\":\"\",\"doi\":\"10.1016/j.cpc.2024.109342\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>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.</p></div>\",\"PeriodicalId\":285,\"journal\":{\"name\":\"Computer Physics Communications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":7.2000,\"publicationDate\":\"2024-08-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computer Physics Communications\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0010465524002650\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Physics Communications","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0010465524002650","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
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.
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.