Computer Model Calibration with Large Spatial Outputs

The Bayesian computer model calibration method has proven to be effective in a wide range of applications. In this framework, input parameters are tuned by comparing model outputs to observations. However, this methodology becomes computationally expensive for large spatial model outputs. To overcome this challenge, we employ a truncated basis representations of the model outputs. We then aim to match the model outputs coefficients with the coefficients from observations in the same basis; we also optimize the truncation level. In a second step, we enhance the calibration with the addition of the INLA-SPDE technique. We embed nonstationary behavior and derivative information of the spatial field into the calibration by inserting two INLA-SPDE parameters into the calibration. Several synthetic examples and a climate model illustration highlight the benefits of our approach for model outputs distributed over the plane or the sphere.