Model Calibration via Deformation

Dynamical computer models often exhibit space-time features that are partially misaligned or misshapen when compared to observational data. Whether due to approximate numerical schemes, incomplete physics, or estimated boundary conditions, the goal of calibrating these models to field data involves optimally aligning model output with observed features. The traditional approach to correcting model discrepancy is to introduce an additive and/or multiplicative bias. Especially for dynamical models, systematic bias may alternatively be viewed as deformation bias. We introduce an expanded approach to model calibration in the presence of space-time feature discrepancy. Borrowing ideas from the image warping literature, we propose a nonlinear deformation of the computer model that optimally aligns with observed images; probabilistically this manifests as a transformation of model coordinate space with a variational penalty on the likelihood function. We apply the approach to a dynamical magnetosphere-ionosphere computer model that exhibits challenging feature discrepancies, and we successfully identify a region of input parameter space that simultaneously minimizes model error and discrepancy from field data.