Sampling-based surrogate likelihood inference for spatial warping error models with applications to aerosol simulations

Music City Center 

Complex simulators of physical processes are used increasingly often for scientific applications. However, the parameters governing these physical processes can be highly uncertain so reducing this uncertainty is important for improving the accuracy of simulator predictions. To this end, a growing amount of work focuses on constraining these physical parameters by comparing the simulator outputs to corresponding real-world observations. However, these simulators can often be systematically misspecified which requires accounting for this model discrepancy when inferring model parameters. Existing work does this by incorporating a data-driven additive model discrepancy error but this treatment does not necessarily represent how we expect many simulators to be misspecified. In particular, for simulators that output spatial fields, we hypothesize that misspecification could lead to spatial warping errors between the simulation and observations where the simulated structure of a spatial feature may be correct overall but it is displaced in space or distorted in shape. To address this, we propose a novel spatiotemporal modeling framework and estimation procedure that models the spatial warping errors as random transport maps that capture these spatial distortions. Our method generates plausible transport maps using convex Gaussian processes that preserve the spatial structure of the simulation. However, using this shape-constrained process results in a challenging likelihood-free inference problem. We demonstrate how inference is nevertheless possible using sampling-based surrogate likelihoods which we estimate and maximize using exact Hamiltonian Monte Carlo sampling and Neural Likelihood techniques. As a concrete application of our methodology, we consider the UKESM1 climate model and remotely sensed aerosol observations where we expect misspecification in atmospheric dynamics or meteorology to lead to spatial warping errors. Our results show that modeling spatial warping errors yields significantly higher likelihoods and stronger parameter-constraining capabilities compared to models that rely solely on additive errors.