用神经过程实现物理模型的高效校准，快速适配新系统并量化不确定性。
APIC: Amortized Physics-Informed Calibration using Neural Processes
- 通过双分支潜空间分离具体参数与共性偏差，实现群体级校准
- 在弹簧振子、捕食者-猎物系统等场景中显著提升参数恢复精度
- 适合需要快速泛化到新系统的物理建模研究者使用
物理模型因机制缺失或误设而存在系统性偏差，导致预测与真实观测不一致。传统肯尼迪-奥黑根（KOH）框架虽能显式建模偏差，但其逐实例非摊销形式难以扩展至相关系统族。本文提出摊销式物理信息校准（APIC），基于神经过程构建群体级贝叶斯推断框架，可跨实例高效校准。该方法采用双分支潜空间结构，将实例特异性物理参数与共享的状态依赖偏差解耦。通过将可微分物理模型嵌入摊销推理主干，APIC仅需稀疏观测即可快速校准未见实例，并提供不确定性估计。在阻尼弹簧振子、洛特卡-沃尔泰拉系统及错设物理参数的对流-扩散偏微分方程上验证，相比其他校准方法，本方法在参数恢复和系统性偏差结构识别上均表现更优。
原文摘要 · Abstract (English)
Physics models are inherently imperfect due to misspecified or missing mechanisms, resulting in systematic discrepancies between model predictions and real-world observations. The Kennedy-O'Hagan (KOH) framework addresses this issue through explicit discrepancy modeling. However, its non-amortized, per-instance formulation limits scalability across families of related systems. We introduce Amortized Physics-Informed Calibration (APIC), a population-level extension of KOH that leverages Neural Processes to perform scalable Bayesian inference across realizations. Our framework employs a two-branch latent architecture to disentangle instance-specific physical parameters from shared, state-dependent structural discrepancies. By integrating differentiable physics into an amortized inference backbone, APIC enables rapid calibration of unseen realizations from sparse observations while quantifying uncertainty. Experiments on the damped spring oscillator, the Lotka-Volterra system, and the advection-diffusion PDE with misspecified physics demonstrate improved parameter recovery and consistent identification of the systemic discrepancy structure compared to other calibration approaches.
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