Neural Likelihood for Spatial Transport Error Models with Applications to Aerosol Parameter Constraints

Complex simulators of physical processes are used increasingly often for scientific applications. We propose a novel spatiotemporal modeling framework that models spatial transport errors as random transport maps that capture 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, which we overcome using exact Hamiltonian Monte Carlo sampling and Neural likelihood techniques. We apply our methodology to the UKESM1 climate model and remotely sensed aerosol observations.

Jun 18, 2026