Efficient Bayesian calibration of many-parameter system models

Computer models of complex engineering systems rely on proper tuning of their model parameters to ensure accurate predictions of the system behavior. The challenge of effectively calibrating many-parameter models is the difficulty of sampling in high-dimensional spaces and the computational expense of generating a large number of samples to characterize the calibrated parameter distributions. The method of active subspaces has been shown to be effective at constructing low-dimensional latent spaces for Bayesian inverse problems when the misfit function (i.e., negative log-likelihood) is treated as the function of interest. On the other hand, works that implement surrogate modeling for inference often focus on approximating the predictive model itself. In this work, an integrated dimension reduction and surrogate modeling framework for efficient and robust model calibration based on the Kennedy O'Hagan framework is proposed, with the following key components. First, an active subspace of the misfit function is identified. Then, a surrogate model for the misfit is constructed in this low-dimensional latent space. Care is taken to ensure that the assumed probabilistic structure of the misfit surrogate is compatible with the structure imposed on the misfit by the observation noise and computer model discrepancy. Further, a generalized likelihood function is defined that can account for the misfit surrogate uncertainty along with the other usual sources of uncertainty, e.g., experimental noise, model inadequacy, etc. This general formulation is shown to be valid for surrogates of any deterministic bijective function of the original likelihood, not just the misfit. Finally, a strategy for incorporating the uncertainty in identifying the active subspace is included.