Computer Model Calibration Using the Ensemble Kalman Filter

Abstract

Computer model calibration is the process of determining input parameter settings to a computational model that are consistent with physical observations. This is often quite challenging due to the computational demands of running the model. In this article, we use the ensemble Kalman filter (EnKF) for computer model calibration. The EnKF has proven effective in quantifying uncertainty in data assimilation problems such as weather forecasting and ocean modeling. We find that the EnKF can be directly adapted to Bayesian computer model calibration. It is motivated by the mean and covariance relationship between the model inputs and outputs, producing an approximate posterior ensemble of the calibration parameters. While this approach may not fully capture effects due to nonlinearities in the computer model response, its computational efficiency makes it a viable choice for exploratory analyses, design problems, or problems with large numbers of model runs, inputs, and outputs.

KEY WORDS:

• Bayesian statistics
• Computer experiments
• Data assimilation
• Gaussian process
• Model validation
• Parameter estimation
• Uncertainty quantification

ACKNOWLEDGMENTS

We thank the reviewers, Associate Editor, and Editor for many helpful comments on earlier drafts. This work was supported in part by the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, and Scientific Discovery through Advanced Computing (SciDAC) program.