Blade：一种使用扩散先验的无导数贝叶斯反演方法
Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priors
AI总结：
本文提出Blade方法，通过使用扩散模型作为数据驱动的先验，解决无导数贝叶斯反演中高维非线性问题的后验估计问题，实现了准确且校准良好的后验分布。
摘要：
无导数贝叶斯反演在科学和工程应用中出现，特别是在正向模型成本高或无法通过导数进行微分时。现有的无导数方法将后验缩减为点估计或在高维非线性问题中返回严重过自信的不确定性。我们介绍了Blade，它使用相互作用粒子的集合产生准确且校准良好的后验。Blade利用扩散模型作为数据驱动的先验，并且只通过正向评估（即无导数）查询正向模型。理论上，我们证明了在正向模型近似和先验分数估计误差下，Blade的收敛性和稳定性。经验上，在非线性流体动力学中，Blade产生校准良好的后验样本，这些样本现有无导数方法无法产生，通过CRPS、扩展-技能比和等级直方图进行测量。其准确性和校准随着迭代次数和粒子数的增加而持续提高，这得到了我们的收敛性和稳定性分析以及经验实验的支持。
英文摘要：
Derivative-free Bayesian inversion arises in science and engineering applications, particularly when forward model is costly or infeasible to differentiate through. Existing derivative-free methods collapse the posterior to a point estimate or return severely over-confident uncertainty on high-dimensional, nonlinear problems. We introduce Blade, which produces accurate and well-calibrated posteriors using an ensemble of interacting particles. Blade leverages diffusion models as data-driven priors, and only queries the forward model through forward evaluations (i.e., derivative-free). Theoretically, we show the convergence and stability of Blade under forward model approximation and prior score estimation error. Empirically, on nonlinear fluid dynamics, Blade produces well-calibrated posterior samples that existing derivative-free methods cannot, as measured by CRPS, the spread-skill ratio, and the rank histogram. Its accuracy and calibration improve consistently with more iterations and particles, backed by our convergence and stability analysis and empirical experiments.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
