BISIP: Bias-Guided Stochastic Search for Simulation-Based Inverse Problems

Complex simulations, common in science and engineering, lead to challenging inverse problems. Bayesian methods, in particular deep learning-based ones, are widely used but are limited by data scarcity, computational cost of simulations, and distribution shift during testing. To address these challenges, we develop a stochastic search-based method to iteratively refine the inverse estimate. We use forward-consistency to estimate model bias, which, together with the model variance, guides the active acquisition of training samples to improve inverse estimation during testing. We evaluate the proposed approach on inverse problems of increasing complexity, including linear inverse with heteroscedastic noise, inverse Laplace transform, and non-linear reconstruction of neutral hydrogen distribution in the early universe from sparse cosmological observations. Across the evaluated settings, our method consistently improves inverse estimation compared with the considered active-learning and sequential inference baselines. In the cosmological reconstruction task, BISIP achieves the lowest estimation error among the evaluated methods while requiring substantially fewer simulator evaluations.