Manifold learning for coarse-graining atomistic simulations: Application to amorphous solids
Manifold learning for coarse-graining atomistic simulations: Application to amorphous solids
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DOI：
10.1016/j.actamat.2021.117008
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发表时间：
2021-03
期刊：
影响因子：
9.4
通讯作者：
Katiana Kontolati;Darius D. Alix-Williams;Nicholas M. Boffi;M. Falk;C. Rycroft;M. Shields
中科院分区：
文献类型：
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作者：
Katiana Kontolati;Darius D. Alix-Williams;Nicholas M. Boffi;M. Falk;C. Rycroft;M. Shields
我们引入了一个广义的机器学习框架的概率参数化上尺度模型的形式，非线性偏微分方程符合连续理论，基于粗粒度的原子模拟数据的机械变形和流动过程。该框架采用了一种假设的粗粒度方法与流形学习和基于代理的优化技术。描述多尺度模型的感兴趣的数量的粗粒度高维数据被投影到一个非线性流形上，其几何和拓扑结构被利用来测量流形距离形式的行为差异。使用高斯过程回归构建代理模型，以识别随机参数和距离之间的映射。采用无导数优化来自适应地识别能够快速再现系统的行为，同时保持与粗粒度原子级模拟的一致性的上尺度模型的唯一参数集。所提出的方法被应用到学习的剪切转变区（STZ）塑性理论，描述在无定形固体的塑性变形，以及粗粒化参数之间的原子和连续表示需要转换的参数。我们表明，该方法能够成功地将粗粒度的微观模拟与宏观尺度的可观测量联系起来，并在不同尺度的模型之间实现高水平的奇偶校验。
We introduce a generalized machine learning framework to probabilistically parameterize upper-scale models in the form of nonlinear PDEs consistent with a continuum theory, based on coarse-grained atomistic simulation data of mechanical deformation and flow processes. The proposed framework utilizes a hypothesized coarse-graining methodology with manifold learning and surrogate-based optimization techniques. Coarse-grained high-dimensional data describing quantities of interest of the multiscale models are projected onto a nonlinear manifold whose geometric and topological structure is exploited for measuring behavioral discrepancies in the form of manifold distances. A surrogate model is constructed using Gaussian process regression to identify a mapping between stochastic parameters and distances. Derivative-free optimization is employed to adaptively identify a unique set of parameters of the upper-scale model capable of rapidly reproducing the system’s behavior while maintaining consistency with coarse-grained atomic-level simulations. The proposed method is applied to learn the parameters of the shear transformation zone (STZ) theory of plasticity that describes plastic deformation in amorphous solids as well as coarse-graining parameters needed to translate between atomistic and continuum representations. We show that the methodology is able to successfully link coarse-grained microscale simulations to macroscale observables and achieve a high-level of parity between the models across scales.