发表机构
TU Graz（格拉茨工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究揭示贝叶斯物理信息神经网络（B-PINNs）的碰撞器偏差问题，提出层次链模型结合粒子MCMC方法修正偏差，经实验验证其有效性。
AI 中文摘要
贝叶斯物理信息神经网络（Bayesian physics-informed neural networks, B-PINNs）是一种从稀疏或带噪声观测中进行参数与状态推断的流行框架。它通常通过碰撞器结构构建，其中物理参数与轨迹参数被假设为先验独立，并通过微分方程残差上的虚拟似然耦合，以强制物理一致性。我们表明，这种建模选择会在物理参数的后验中引发严重的系统性偏差：即使先验有利地集中在真实参数附近，所得后验也可能漂移并远离真实参数。作为解决方案，我们提出一种层次链模型，其中物理过程生成轨迹，轨迹进而生成观测。该链模型不会出现这种后验偏差，但由于存在依赖物理的归一化常数，它会带来更困难的所谓双难解推断问题。这一挑战可通过离散化基础随机动力学解决，之后可使用粒子马尔可夫链蒙特卡洛（particle MCMC）精确采样链后验。我们确定了表征碰撞器偏差的两种不同机制，推导了其幅度的解析近似，并建立了预测标准B-PINNs何时仍可靠的诊断准则。实验证实了预测的偏差，并表明链公式成功避免了该偏差。
英文摘要
Bayesian physics-informed neural networks (B-PINNs) are a popular framework for parameter and state inference from sparse or noisy observations. They are commonly formulated via a collider structure, in which physical and trajectory parameters are assumed to be a priori independent and become coupled through virtual likelihoods on differential-equation residuals that enforce physical consistency. We show that this modeling choice can induce severe systematic bias in the posterior over physical parameters: even when the prior is favorably centered on the ground-truth parameters, the resulting posterior can drift away and concentrate far from them. As a remedy, we advocate a hierarchical chain model in which physics generates trajectories, which in turn generate observations. The chain model does not suffer from this posterior bias, but it poses a harder, so-called doubly intractable, inference problem due to a physics-dependent normalization constant. This challenge can be resolved by discretizing the underlying stochastic dynamics, after which the chain posterior can be sampled exactly with particle MCMC. We identify two distinct mechanisms characterizing the collider bias, derive analytical approximations of their magnitudes, and establish diagnostic criteria for predicting when standard B-PINNs remain reliable. Experiments confirm the predicted bias and show that the chain formulation successfully avoids it.
