基于主动扩散的不完备先验下不适定逆问题推理方法
Active Diffusion-Based Inference for Ill-Posed Inverse Problems under Incomplete Priors
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中文总结 AI 辅助
该研究针对不完备先验下的不适定逆问题，提出主动扩散模型求解器，通过后验不确定性修正模型误设，在两类任务上验证了其鲁棒推理的有效性。
中文摘要 AI 辅助
许多科学与工程应用需要从实验可观测数据中估计未知参数——这类逆问题因非线性、噪声和不适定性而固有地具有挑战性。本文提出一种基于主动扩散的逆问题求解器：训练扩散模型（DM）学习参数空间与可观测空间之间的映射，通过后验不确定性迭代检测并修正模型误设，即使初始训练边界未包含真实参数，该方法也能发现并学习参数空间的正确区域。这为自适应域扩充提供了原则性贝叶斯依据，确保在不完备先验知识下对逆问题的鲁棒推理。我们在具有无穷多解的玩具逆问题，以及量子色动力学核子结构分析中量子关联函数到事例可观测量的参数化任务上，验证了该逆求解器的有效性。
英文摘要
Many scientific and engineering applications require estimating unknown parameters from experimentally observable data -- an inverse problem that is inherently challenging due to nonlinearity, noise, and ill-posedness. In this paper, we propose an active diffusion-based inverse problem solver. A DM is trained to learn the mapping between the parameter space and the observable space. By iteratively detecting and correcting model misspecification through posterior uncertainty, the method discovers and learns the correct region of parameter space, even when initial training bounds exclude the true parameters. This provides a principled, Bayesian justification for adaptive domain augmentation and ensures robust inference for inverse problems under incomplete prior knowledge. We demonstrate the effectiveness of our inverse solver for a toy inverse problem with infinite solutions, and for the parameterization of the quantum correlation functions to event observables in a Quantum Chromodynamics analysis of nucleon structure.
发表机构
- Old Dominion University（奥多明尼昂大学）
- Jefferson Lab（杰斐逊实验室）
机构由 AI 辅助整理，请以论文原文为准。
