  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.
