AI 中文总结
针对部分观测动态生物系统不确定性量化难题，提出结合留一法折刀法+经验校准与高斯不确定性传播的混合框架及CUQDyn1 Plus软件，能进行全局参数估计等，验证表明其为实用高效的UQ工作流程，可补充贝叶斯工作流程。
AI 中文摘要
机械常微分方程（ODE）模型在系统生物学中广泛应用，但当仅实验观测部分状态变量时，不确定性量化（UQ）仍很困难。现有贝叶斯和基于似然的方法对非线性、弱可识别或高维系统计算要求高。我们提出了一个用于部分观测ODE系统UQ的框架及其相应软件CUQDyn1 Plus。我们的方法将观测状态的留一法折刀法+式经验校准与隐藏状态的基于灵敏度的高斯不确定性传播相结合。软件支持全局参数估计、协方差传播、自举重采样轨迹不确定性和基于模拟的校准等。在六个基准系统上的验证表明，在条件良好的情况下行为准确，在非线性、弱可识别性或全局分支切换不可识别性下模型会退化。CUQDyn1 Plus为具有观测和潜在状态的系统生物学模型提供了实用且计算高效的UQ工作流程，其诊断输出有助于确定何时局部高斯传播可靠以及何时应谨慎解释不确定性带，是完全贝叶斯工作流程的有用补充。
英文摘要
Mechanistic ordinary differential equation (ODE) models are widely used in systems biology, but uncertainty quantification (UQ) remains difficult when only a subset of state variables is experimentally observed. Existing Bayesian and likelihood-based approaches can be computationally demanding for nonlinear, weakly identifiable, or high-dimensional systems. We present a framework, and its corresponding software CUQDyn1 Plus, for UQ in partially observed ODE systems. Our method combines leave-one-out jackknife+-style empirical calibration for observed states with sensitivity-based Gaussian uncertainty propagation for hidden states. The software supports global parameter estimation, covariance propagation, bootstrap trajectory uncertainty and simulation-based calibration. It also facilitates comparison with Bayesian workflows, automated reporting, and reproducibility diagnostics. Validation on six benchmark systems shows accurate behavior in well-conditioned cases and model-dependent degradation under nonlinearity, weak identifiability, or global branch-switching non-identifiability. CUQDyn1 Plus provides a practical and computationally efficient UQ workflow for systems biology models with observed and latent states. Its diagnostic outputs help identify when local Gaussian propagation is reliable and when uncertainty bands should be interpreted cautiously, making it a useful complement to fully Bayesian workflows.
