Computer simulation models are widely used to study complex physical systems. A related fundamental topic is the inverse problem, also called calibration, which aims at learning about the values of parameters in the model based on observations. In most real applications, the parameters have specific physical meanings, and we call them physical parameters. To recognize the true underlying physical system, we need to effectively estimate such parameters. However, existing calibration methods cannot do this well due to the model identifiability problem. This paper proposes a semi-parametric model, called the discrepancy decomposition model, to describe the discrepancy between the physical system and the computer model. The proposed model possesses a clear interpretation, and more importantly, it is identifiable under mild conditions. Under this model, we present estimators of the physical parameters and the discrepancy, and then establish their asymptotic properties. Numerical examples show that the proposed method can better estimate the physical parameters than existing methods.

中文翻译：

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物理参数校准

计算机仿真模型广泛用于研究复杂的物理系统。一个相关的基本主题是逆问题，也称为校准，其目的是根据观察了解模型中的参数值。在大多数实际应用中，参数都有特定的物理含义，我们称之为物理参数。为了识别真正的底层物理系统，我们需要有效地估计这些参数。然而，由于模型可识别性问题，现有的校准方法不能很好地做到这一点。本文提出了一种半参数模型，称为差异分解模型，用于描述物理系统与计算机模型之间的差异。所提出的模型具有清晰的解释，更重要的是，它在温和的条件下是可识别的。在这个模型下，我们提出了物理参数和差异的估计量，然后建立它们的渐近特性。数值例子表明，所提出的方法比现有方法可以更好地估计物理参数。