标题： 可信的生成模型反问题科学推断 显示英文标题

标题： Trustworthy scientific inference for inverse problems with generative models

摘要： 生成式人工智能（AI）通过从训练示例中学习模式，擅长生成复杂的数据结构（文本、图像、视频）。 在各个科学领域，研究人员现在正在将生成模型应用于“反问题”，以从观测数据中推断隐藏参数。 虽然这些方法可以处理难以处理的模型和大规模研究，但它们也可能产生有偏见或过于自信的结论。 我们提出了一种解决方案，即频率学派-贝叶斯（FreB），这是一种数学严谨的协议，能够将AI生成的概率分布重新塑造为置信区域，这些区域以预期的概率一致地包含真实参数，同时在训练数据和目标数据一致时达到最小尺寸。 我们通过在物理科学中解决各种案例研究来展示FreB的有效性：在数据集转移下识别未知源，调和竞争性理论模型，以及减轻观察研究中的选择偏差和系统误差。 通过提供具有可解释诊断的有效性保证，FreB使在直接似然评估仍然不可能或代价高昂的领域中实现可信的科学推断成为可能。 显示英文摘要

摘要： Generative artificial intelligence (AI) excels at producing complex data structures (text, images, videos) by learning patterns from training examples. Across scientific disciplines, researchers are now applying generative models to ``inverse problems'' to infer hidden parameters from observed data. While these methods can handle intractable models and large-scale studies, they can also produce biased or overconfident conclusions. We present a solution with Frequentist-Bayes (FreB), a mathematically rigorous protocol that reshapes AI-generated probability distributions into confidence regions that consistently include true parameters with the expected probability, while achieving minimum size when training and target data align. We demonstrate FreB's effectiveness by tackling diverse case studies in the physical sciences: identifying unknown sources under dataset shift, reconciling competing theoretical models, and mitigating selection bias and systematics in observational studies. By providing validity guarantees with interpretable diagnostics, FreB enables trustworthy scientific inference across fields where direct likelihood evaluation remains impossible or prohibitively expensive.