发表机构
University of South Carolina（南卡罗来纳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对耦合ODE系统在模型失配下的校准难题，提出基于灵敏度的自动结构约束框架，无需特定先验，提升可辨识性与预测精度，并在三个模型上验证。
AI 中文摘要
常微分方程（ODE）耦合系统被广泛用于模拟复杂的物理和生物过程。在这些应用中，必须将ODE模型参数校准到现场数据，以实现预测和参数推断。在实践中，控制方程是对真实系统的不完美近似，导致不可忽略的模型失配，必须将其纳入以避免有偏的参数估计。然而，众所周知，高度灵活的失配模型可能混淆失配和模拟器参数，导致可辨识性差。因此，实践者通常必须施加特定于问题的先验约束，以充分正则化失配，这可能具有挑战性和繁琐性。在这项工作中，我们提出了一种新颖的校准框架，用于耦合、多输出ODE系统，该框架对失配施加自动的、模型结构的约束，提高了可辨识性，而无需特定应用的失配先验。前向模型梯度通过灵敏度方程计算，与ODE系统作为耦合初值问题联合求解。后验推断使用针对所得约束后验定制的自适应Metropolis-within-Gibbs采样器进行。我们在三个模型系统上演示了该方法：质量-弹簧振荡器、传染病传播模型和神经元放电模型。我们表明，与标准校准方法相比，我们的方法导致改进的参数推断和预测准确性。
英文摘要
Coupled systems of ordinary differential equations (ODEs) are widely used to model complex physical and biological processes. In these applications, ODE model parameters must be calibrated to field data to enable prediction and parameter inference. In practice, the governing ODEs are an imperfect approximation to the true system, leading to non-negligible model discrepancy that must be incorporated to avoid biased parameter estimates. However, it is well known that highly flexible discrepancy models can confound discrepancy and simulator parameters, leading to poor identifiability. As a result, practitioners often must impose problem-specific prior constraints to adequately regularize the discrepancy, which can be challenging and cumbersome. In this work, we propose a novel calibration framework for coupled, multi-output ODE systems that enforces automatic, model-structural constraints on the discrepancy, improving identifiability without requiring application-specific discrepancy priors. Forward-model gradients are computed via sensitivity equations, solved jointly with the ODE system as a coupled initial value problem. Posterior inference is performed using an adaptive Metropolis-within-Gibbs sampler tailored to the resulting constrained posterior. We demonstrate the approach on three model systems: a mass-spring oscillator, a model of infectious disease spread, and a neuron firing model. We show that our method leads to improved parameter inference and predictive accuracy compared to standard calibration approaches.
Comments33 pages, 13 figures
