Variational system identification of the partial differential equations governing microstructure evolution in materials: Inference over sparse and spatially unrelated data

Wang Z.; Huan X.; Garikipati K.

摘要

Pattern formation is a widely observed phenomenon in diverse fields including materials physics, developmental biology and ecology, among many others. The physics underlying the patterns is specific to the mechanisms, and is encoded by partial differential equations (PDEs). With the aim of discovering hidden physics, we have previously presented a variational approach to identifying such systems of PDEs in the face of noisy data at varying fidelities (Computer Methods in Applied Mechanics and Engineering, 356:44-74, 2019). Here, we extend our variational system identification methods to address the challenges presented by image data on microstructures in materials physics. PDEs are formally posed as initial and boundary value problems over combinations of time intervals and spatial domains whose evolution is either fixed or can be tracked. However, the vast majority of microscopy techniques for evolving microstructure in a given material system deliver micrographs of pattern evolution over domains that bear no relation with each other at different time instants. The temporal resolution can rarely capture the fastest time scales that dominate the early dynamics, and noise abounds. Furthermore, data for evolution of the same phenomenon in a material system may well be obtained from different physical specimens. Against this backdrop of spatially unrelated, sparse and multi-source data, we exploit the variational framework to make judicious choices of weighting functions and identify PDE operators from the dynamics. A consistency condition arises for parsimonious inference of a minimal set of the spatial operators at steady state. It is complemented by a confirmation test that provides a sharp condition for acceptance of the inferred operators. The entire framework is demonstrated on synthetic data that reflect the characteristics of the experimental material microscopy images. (C) 2021 Elsevier B.V. All rights reserved.

机译：模式形成是在不同领域中广泛观察到的现象，包括材料物理，发育生物学和生态学，其中许多其他领域。模式下面的物理学特定于机制，并且由部分微分方程（PDE）编码。随着发现隐藏物理的目的，我们之前提出了一种变分方法，以在不同保真度下识别面对嘈杂数据中这种PDE的系统（应用力学和工程中的计算机方法，356：44-74,2019）。在这里，我们扩展了各种系统识别方法，以解决通过材料物理学中的微观结构上的图像数据提出的挑战。 PDE在正式构成为初始和边值问题，而不是时间间隔和空间域的组合，其演进是固定的或可以被跟踪的。然而，绝大多数用于在给定材料系统中演化微观结构的显微镜技术提供了在不同时间瞬间在不同时间瞬间彼此不相关的结构演变的显微照片。时间分辨率很少捕获主导早期动态的最快时间尺度，并且噪音比比皆是。此外，可以从不同的物理标本获得材料系统中相同现象的演化数据。在空间不相关的，稀疏和多源数据的情况下，我们利用变分框架来使加权函数的明智选择并从动态识别PDE运算符。产生一致性条件，用于在稳态下的最小空间运算符的显着推断。它是通过确认测试的补充，提供了敏锐的条件，以接受推断的运营商。整个框架在反映实验材料显微镜图像的特性的合成数据上证明了整个框架。（c）2021 Elsevier B.v.保留所有权利。

Variational system identification of the partial differential equations governing microstructure evolution in materials: Inference over sparse and spatially unrelated data

摘要

著录项

相关主题

期刊订阅