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Physical Parameter Calibration

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.