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.

翻译：计算机仿真模型被广泛应用于研究复杂物理系统。一个相关的基础问题是逆问题，也称为校准，其目标是根据观测数据学习模型中参数的值。在实际应用中，这些参数通常具有特定的物理含义，我们称之为物理参数。为了准确识别真实的物理系统，需要有效估计这些参数。然而，由于模型可辨识性问题，现有校准方法难以实现这一目标。本文提出一种半参数模型——偏差分解模型，用于描述物理系统与计算机模型之间的偏差。该模型具有清晰的解释性，更重要的是，在温和条件下具有可辨识性。基于该模型，我们给出了物理参数与偏差的估计量，并建立了它们的渐近性质。数值算例表明，所提出的方法比现有方法能更有效地估计物理参数。