标题： 流形学习用于原子模拟的粗粒化：非晶固体的应用 显示英文标题

标题： Manifold learning for coarse-graining atomistic simulations: Application to amorphous solids

摘要： 我们引入了一个广义的机器学习框架，以概率方式参数化符合连续介质理论的非线性偏微分方程形式的上尺度模型，该框架基于机械变形和流动过程的粗粒度原子模拟数据。 所提出的框架利用了一个假设的粗粒化方法，结合流形学习和基于代理模型的优化技术。 描述多尺度模型感兴趣量的粗粒度高维数据被投影到一个非线性流形上，该流形的几何和拓扑结构被用于以流形距离的形式测量行为差异。 使用高斯过程回归构建一个代理模型，以识别随机参数与距离之间的映射关系。 采用无导数优化方法，自适应地确定一组唯一的上尺度模型参数，这些参数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。 所提出的方法被应用于学习塑性剪切转变区（STZ）理论的参数，该理论描述了非晶固体中的塑性变形，以及在原子尺度和连续介质表示之间转换所需的粗粒化参数。 我们证明该方法能够成功地将粗粒度微观模拟与宏观可观测量联系起来，并在不同尺度的模型之间实现高水平的一致性。 显示英文摘要

摘要： 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.