教你怎么用变分推断做物理驱动的生成建模与不确定性分析
A Primer on Variational Inference for Physics-Informed Deep Generative Modelling
- 基于变分推断构建物理约束下的生成模型框架
- 实现前向与反演问题的高效不确定性量化
- 适合需要可信推断的科研人员学习应用
变分推断（VI）是一种计算高效且可扩展的近似贝叶斯推断方法，在不确定性量化与实际可行性之间取得平衡。其内置贝叶斯正则化与灵活性使其在生成建模与反演任务中表现优异，特别适用于物理相关问题。由于物理模型决定了变量间的依赖关系，因此需针对性推导核心的VI学习目标。在许多物理推断场景中，这种结构具有深层意义，对准确捕捉动态过程至关重要。本文为科学界提供了一篇清晰完整的技术导引，涵盖标准VI推导及其在深度学习中的实现方式，并综述与统一了近期文献中展示的VI灵活性。本论文面向希望以不确定性量化为核心解决物理问题的广泛科学读者。
原文摘要 · Abstract (English)
Variational inference (VI) is a computationally efficient and scalable methodology for approximate Bayesian inference. It strikes a balance between accuracy of uncertainty quantification and practical tractability. It excels at generative modelling and inversion tasks due to its built-in Bayesian regularisation and flexibility, essential qualities for physics related problems. For such problems, the underlying physical model determines the dependence between variables of interest, which in turn will require a tailored derivation for the central VI learning objective. Furthermore, in many physical inference applications this structure has rich meaning and is essential for accurately capturing the dynamics of interest. In this paper, we provide an accessible and thorough technical introduction to VI for forward and inverse problems, guiding the reader through standard derivations of the VI framework and how it can best be realized through deep learning. We then review and unify recent literature exemplifying the flexibility allowed by VI. This paper is designed for a general scientific audience looking to solve physics-based problems with an emphasis on uncertainty quantification
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