We describe and compare two formulations of inverse problems for a physics-based process model in the context of uncertainty and random variability: the Bayesian inverse problem and the stochastic inverse problem. We describe the foundations of the two problems in order to create a context for interpreting the applicability and solutions of inverse problems important for scientific and engineering inference. We conclude by comparing them to statistical approaches to related problems, including Bayesian calibration of computer models.

中文翻译：

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基于物理的过程模型的逆问题


在不确定性和随机可变性的背景下，我们描述并比较了基于物理的过程模型的逆问题的两种公式：贝叶斯逆问题和随机逆问题。我们描述了这两个问题的基础，以便为解释对科学和工程推理很重要的逆问题的适用性和解决方案创建一个上下文。我们通过将它们与相关问题的统计方法进行比较来得出结论，包括计算机模型的贝叶斯校准。