Not All Observations Are Equal: Guiding Derivative-Free Ensembles via Uncertainty Contraction

Ensemble Kalman Guidance (EnKG) is attractive for high-dimensional inverse problems, especially with black-box physical forward models where repeated gradient computation is difficult or impractical, as it only requires forward evaluations. However, its empirical performance can be hindered by the finite ensemble size when the parameter dimension is large, resulting in unreliable or biased estimates. To address this issue, we propose Uncertainty-Contraction Ensemble Guidance (UCEG), a monitor-guided adaptive sampling framework that improves the quality of the ensemble correction without increasing the ensemble size. UCEG treats guidance construction as an observation-selection problem and uses update activity as a practical proxy for local uncertainty contraction in the finite-ensemble correction, retaining informative observations while suppressing uninformative ones. Experiments on challenging inverse problems including full waveform inversion (FWI) and Navier–Stokes show that UCEG can outperform the corresponding full-observation correction using fewer observations, with faster inference when observation subsampling reduces evaluation cost.