We present a novel method for generating sequential parameter estimates and quantifying epistemic uncertainty in dynamical systems within a data-consistent (DC) framework. The DC framework differs from traditional Bayesian approaches due to the incorporation of the push-forward of an initial density, which performs selective regularization in parameter directions not informed by the data in the resulting updated density. This extends a previous study that included the linear Gaussian theory within the DC framework and introduced the maximal updated density (MUD) estimate as an alternative to both least squares and maximum a posterior (MAP) estimates. In this work, we introduce algorithms for operational settings of MUD estimation in real or near-real time where spatio-temporal datasets arrive in packets to provide updated estimates of parameters and identify potential parameter drift. Computational diagnostics within the DC framework prove critical for evaluating (1) the quality of the DC update and MUD estimate and (2) the detection of parameter value drift. The algorithms are applied to estimate (1) wind drag parameters in a high-fidelity storm surge model, (2) thermal diffusivity field for a heat conductivity problem, and (3) changing infection and incubation rates of an epidemiological model.

翻译：我们提出了一种新颖方法，用于在数据一致性（DC）框架内生成动态系统的序贯参数估计并量化认知不确定性。与传统贝叶斯方法不同，DC框架通过融入初始密度的前推机制，对未受数据影响的参数方向实施选择性正则化，从而在最终更新密度中实现约束。该研究扩展了先前的工作——该工作在线性高斯理论下将DC框架与贝叶斯推断关联，并引入最大更新密度（MUD）估计作为最小二乘估计和最大后验（MAP）估计的替代方案。本文针对实时或近实时操作场景提出了MUD估计算法，在此类场景中，时空数据集以数据包形式到达，用于提供参数更新估计并识别潜在参数漂移。DC框架内的计算诊断方法对于评估以下两点至关重要：（1）DC更新与MUD估计的质量；（2）参数值漂移的检测。该算法被应用于三个案例：（1）高保真风暴潮模型中的风阻参数估计；（2）热传导问题中的热扩散系数场估计；（3）流行病学模型中感染率与潜伏期的时变参数估计。