Robust Ensemble Guidance for Scientific Inverse Problems

2026-10-04

AI Summary

This study addresses the degradation of reconstruction accuracy in ensemble-guided methods for scientific inverse problems caused by observation variance and residual outliers. We propose a robust ensemble guidance approach that introduces a prediction-variance-based weighting mechanism to balance observation scales and adaptively clips normalized residuals to suppress outliers, enhancing solver robustness without requiring additional evaluations of denoisers or forward models. By integrating diffusion models, statistical risk theory, and black-box physics simulators, we validate the method on black hole imaging, Navier-Stokes equations, and acoustic full-waveform inversion tasks. Results demonstrate improvements of 6.2–8.2 dB in PSNR for black hole reconstruction and a 26.4% reduction in fluid dynamics error, significantly outperforming existing baselines.

Abstract

Ensemble guidance combines pretrained diffusion priors with black-box forward models to solve inverse problems without differentiating through the physical simulator. However, observation coordinates with large predictive spread or extreme residuals can dominate the ensemble correction, degrading reconstruction accuracy. We show that two simple modifications, weighting and clipping, substantially improve this correction. Our method, Robust Ensemble Guidance (REG), uses ensemble predictive spread to balance observation scales and adaptively clips standardized residuals to limit the influence of extreme discrepancies. Both operations reuse existing particles and forward predictions, requiring no additional denoiser or forward-model evaluations. Under a local linear Gaussian model, we derive conditions for reduced one-step estimation risk, bound the influence of individual observation coordinates, and characterize when these benefits persist with finite ensembles. Experiments on Navier-Stokes inversion, black-hole imaging, and acoustic full-waveform inversion demonstrate improved reconstruction over the underlying ensemble solver. In particular, REG increases black-hole reconstruction PSNR by 6.2-8.2 dB across three observation regimes and reduces Navier-Stokes reconstruction error by 26.4\% in a matched-budget comparison. These findings highlight the importance of observation heterogeneity and residual influence in designing reliable generative solvers for scientific inverse problems.

Problem

• Scientific Inverse Problems
• Ensemble Guidance
• Diffusion Priors
• Observation Heterogeneity
• Reconstruction Accuracy

Innovation

• Ensemble Guidance
• Inverse Problems
• Diffusion Priors
• Robust Estimation
• Scientific Computing