Parameter Estimation via Gaussian Processes and Maximum Likelihood Estimation
Nicholas West, Laura Painton Swiler · 2010
Computer models usually have a variety of parameters that can (and need to) be tuned so that the model better reflects reality. This problem is called calibration and is an inverse problem. We assume that we have a set of observed responses to given inputs in a physical system and a computer model that depends on parameters that models the physical system being studied. It is often the case that many more simulations can be run than experiments conducted, so we typically have many more simulation results (at various parameter values) than experimental results (at the “true” parameter value). In this paper, we use Maximum Likelihood Estimation (MLE) to calibrate model parameters. We assume that the response data is vector-valued, e.g. a response is given as a function of time. We approximate the underlying models with Gaussian Processes (GPs) and fit the parameters of the GPs with MLE. Specifically, we propose a decomposition approach to identify the basis vectors that allows for efficient calculation of the parameters. Experimental data is then used to calibrate the model parameters. This approach is demonstrated on one test problem.