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In complex large-scale systems such as climate, important effects are causedby a combination of confounding processes that are not fully observable. Theidentification of sources from observations of system state is vital forattribution and prediction, which inform critical policy decisions. Thedifficulty of these types of inverse problems lies in the inability to isolatesources and the cost of simulating computational models. Surrogate models mayenable the many-query algorithms required for source identification, but datachallenges arise from high dimensionality of the state and source, limitedensembles of costly model simulations to train a surrogate model, and few andpotentially noisy state observations for inversion due to measurementlimitations. The influence of auxiliary processes adds an additional layer ofuncertainty that further confounds source identification. We introduce aframework based on (1) calibrating deep neural network surrogates to the flowmaps provided by an ensemble of simulations obtained by varying sources, and(2) using these surrogates in a Bayesian framework to identify sources fromobservations via optimization. Focusing on an atmospheric dispersion exemplar,we find that the expressive and computationally efficient nature of the deepneural network operator surrogates in appropriately reduced dimension allowsfor source identification with uncertainty quantification using limited data.Introducing a variable wind field as an auxiliary process, we find that aBayesian approximation error approach is essential for reliable sourceinversion when uncertainty due to wind stresses the algorithm.

Solving High-Dimensional Inverse Problems with Auxiliary Uncertainty via Operator Learning with Limited Data