非线性动力系统中的状态与参数估计的迭代INLA方法
Iterated INLA for State and Parameter Estimation in Nonlinear Dynamical Systems
AI总结：
本文提出一种基于迭代线性化动力模型并结合INLA方法的数据同化新方法，用于非线性动力系统的状态与参数估计，在保持可解释性的同时提升了预测准确性与鲁棒性。
摘要：
数据同化（DA）方法利用源自微分方程的先验来稳健地插值和外推数据。处理高维、非线性PDE先验的流行技术（如集合方法）主要关注状态估计，但在准确学习参数方面可能存在困难。另一方面，基于机器学习的方法能够自然地学习状态和参数，但其适用性可能受限，或产生难以解释的不确定性。受空间统计学中的Integrated Nested Laplace Approximation（INLA，集成嵌套拉普拉斯近似）方法启发，我们提出了一种基于迭代线性化动力模型的DA替代方法。该方法在每次迭代中生成一个高斯马尔可夫随机场，从而能够使用INLA来推断状态和参数。我们的方法可用于任意非线性系统，同时保持可解释性，并且在DA任务上被证明优于现有方法。通过提供一种更细致的非线性PDE先验处理方法，我们的方法在预测中提供了更高的准确性和鲁棒性，特别是在数据稀疏普遍存在的情况下。
英文摘要：
Data assimilation (DA) methods use priors arising from differential equations to robustly interpolate and extrapolate data. Popular techniques such as ensemble methods that handle high-dimensional, nonlinear PDE priors focus mostly on state estimation, however can have difficulty learning the parameters accurately. On the other hand, machine learning based approaches can naturally learn the state and parameters, but their applicability can be limited, or produce uncertainties that are hard to interpret. Inspired by the Integrated Nested Laplace Approximation (INLA) method in spatial statistics, we propose an alternative approach to DA based on iteratively linearising the dynamical model. This produces a Gaussian Markov random field at each iteration, enabling one to use INLA to infer the state and parameters. Our approach can be used for arbitrary nonlinear systems, while retaining interpretability, and is furthermore demonstrated to outperform existing methods on the DA task. By providing a more nuanced approach to handling nonlinear PDE priors, our methodology offers improved accuracy and robustness in predictions, especially where data sparsity is prevalent.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
