Data-consistent inversion is a recently developed measure-theoretic framework for solving a stochastic inverse problem involving models of physical systems. The goal is to construct a probability measure on model inputs (i.e., parameters of interest) whose associated push-forward measure matches (i.e., is consistent with) a probability measure on the observable outputs of the model (i.e., quantities of interest). Previous implementations required the map from parameters of interest to quantities of interest to be deterministic. This work generalizes this framework for maps that are stochastic, i.e., contain uncertainties and variation not explainable by variations in uncertain parameters of interest. Generalizations of previous theorems of existence, uniqueness, and stability of the data-consistent solution are provided while new theoretical results address the stability of marginals on parameters of interest. A notable aspect of the algorithmic generalization is the ability to query the solution to generate independent identically distributed samples of the parameters of interest without requiring knowledge of the so-called stochastic parameters. This work therefore extends the applicability of the data-consistent inversion framework to a much wider class of problems. This includes those based on purely experimental and field data where only a subset of conditions are either controllable or can be documented between experiments while the underlying physics, measurement errors, and any additional covariates are either uncertain or not accounted for by the researcher. Numerical examples demonstrate application of this approach to systems with stochastic sources of uncertainties embedded within the modeling of a system and a numerical diagnostic is summarized that is useful for determining if a key assumption is verified among competing choices of stochastic maps.

中文翻译：

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随机输入到输出映射的数据一致反演

数据一致反演是最近开发的一种测度理论框架，用于解决涉及物理系统模型的随机反演问题。目标是在模型输入（即感兴趣的参数）上构建概率度量，其关联的前推度量与模型的可观察输出（即感兴趣的数量）的概率度量相匹配（即一致）。以前的实现要求从感兴趣的参数到感兴趣的数量的映射是确定性的。这项工作将这个框架推广到随机地图，即包含不确定性和变化，而这些不确定性和变化无法通过感兴趣的不确定参数的变化来解释。先前存在性、唯一性定理的推广，提供了数据一致解决方案的稳定性和稳定性，同时新的理论结果解决了感兴趣参数的边际稳定性。算法泛化的一个显着方面是能够查询解决方案以生成感兴趣参数的独立同分布样本，而无需了解所谓的随机参数。因此，这项工作将数据一致反演框架的适用性扩展到更广泛的问题类别。这包括那些基于纯实验和现场数据的数据，其中只有一部分条件是可控的或可以在实验之间记录的，而基础物理、测量误差和任何其他协变量要么不确定，要么研究人员没有考虑。