科学反问题的鲁棒集成引导

中文摘要 AI 辅助

集成引导将预训练的扩散先验与黑箱前向模型相结合，无需对物理模拟器进行微分即可解决反问题。然而，具有较大预测离散度或极端残差的观测坐标可能主导集成校正，从而降低重建精度。我们证明，两个简单的修改——加权和裁剪——能显著改善这一校正。我们的方法，鲁棒集成引导（REG），利用集成预测离散度来平衡观测尺度，并自适应地裁剪标准化残差以限制极端差异的影响。这两种操作都复用现有的粒子和前向预测，无需额外的去噪器或前向模型评估。在局部线性高斯模型下，我们推导了降低一步估计风险的条件，限制了单个观测坐标的影响，并刻画了这些优势在有限集成下持续存在的情形。在纳维-斯托克斯反演、黑洞成像和声学全波形反演上的实验表明，与底层集成求解器相比，重建效果有所改善。特别是，REG在三种观测机制下将黑洞重建的峰值信噪比（PSNR）提高了6.2-8.2分贝，并在匹配预算比较中将纳维-斯托克斯重建误差降低了26.4%。这些发现强调了观测异质性和残差影响在设计用于科学反问题的可靠生成式求解器中的重要性。

英文摘要

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.

发表机构

• Beijing Jiaotong University（北京交通大学）
• Tsinghua University（清华大学）

机构由 AI 辅助整理，请以论文原文为准。