This article presents an approach for characterizing and estimating statistical dependence between a large number of observables in a composite material system. Conditional regression is carried out using the estimated joint density function, permitting a systematic exploration of interdependence between fine scale and coarse observables that can be used for both prognosis and design of complex material systems. An example demonstrates the integration of experimental data with a computational database. The statistical approach is based on the probabilistic learning on manifolds recently developed by the authors. This approach leverages intrinsic structure detected through diffusion on graphs with projected stochastic differential equations to generate samples constrained to that structure.

中文翻译：

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复合材料系统数字孪生的概率学习和更新

本文介绍了一种表征和估计复合材料系统中大量可观察对象之间的统计依赖性的方法。使用估计的联合密度函数进行条件回归，允许系统探索细尺度和粗观测之间的相互依赖性，可用于复杂材料系统的预测和设计。一个示例演示了实验数据与计算数据库的集成。统计方法基于作者最近开发的流形概率学习。这种方法利用通过在带有投影随机微分方程的图上的扩散检测到的内在结构来生成受限于该结构的样本。