发表机构
University of California Davis; Brigham Young University（加州大学戴维斯分校; 杨百翰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为结合连续数据同化与优化的参数估计算法提供严格论证，证明灵敏度渐近逼近及损失函数满足近似Polyak-Lojasiewicz不等式，从而保证梯度下降收敛，并用数值示例验证。
AI 中文摘要
我们为一种将连续数据同化与通用优化相结合的参数估计算法提供了严格的论证。对于有限维系统，我们严格论证了底层建模动力系统灵敏度的渐近逼近，证明了$L^2$损失函数满足近似的Polyak-Lojasiewicz不等式，并利用该结果论证了所提算法中梯度下降的收敛性。提供的数值示例展示了严格结果的精确性。
英文摘要
We develop a rigorous justification for a parameter estimation algorithm which couples continuous data assimilation to generic optimization. For finite dimensional systems, we provide a rigorous justification of an asymptotic approximation of the sensitivity for the underlying modeled dynamical system, prove that the $L^2$ loss function satisfies an approximate Polyak-Lojasiewicz inequality, and use that result to justify convergence of gradient descent for the proposed algorithm. Numerical examples are provided that demonstrate the precision of the rigorous results.
