A Continuous-Time Ensemble Kalman-Bucy Smoother for Causal Inference and Model Discovery
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用于因果推断与模型发现的连续时间集合 Kalman–Bucy 平滑器
- 研究问题
- 连续时间非线性动力系统中，如何利用未来观测改进历史状态重建，并进一步探索动态关系、作用时间范围和隐藏参数？
- 方法与思路
- 作者利用集合矩重建平滑条件分布，形成无须切线或伴随模型的框架，并结合协方差局部化、膨胀与迭代模型学习。
- 材料陈述的贡献
- 摘要称在线性高斯系统的无限集合极限中恢复精确平滑均值与协方差方程，并在科学模型中展示状态重建和关系发现。
- 阅读关注点
- 核对有限集合近似及正则化的误差，检查非线性情形下的适用范围，并确认所谓因果关系依赖哪些动力学和观测假设。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未经核验；线性高斯极限结论不自动推广至非线性系统，因果识别条件摘要未说明。
原文摘要
Data assimilation (DA) integrates observational information with model predictions to improve state estimation in complex systems. While filtering provides the basis for online forecasts by using only past and present observations, it can exhibit delays and biases when the underlying dynamics evolve rapidly or undergo regime transitions. Smoothing, which additionally incorporates future observations, provides a natural pipeline for hindcasting and reanalysis that yields an uncertainty reduction beyond the filter. This paper introduces an ensemble Kalman--Bucy smoother (EnKBS) for continuous-time DA of nonlinear dynamical systems, where the smoother's conditional distributions are reconstructed using ensemble moments. The result is a derivative-free framework that does not require explicit computation of tangent-linear or adjoint models, which recovers the exact smoothing mean and covariance equations in the infinite-ensemble limit for linear--Gaussian systems. Incorporating standard regularization techniques for high-dimensional systems, such as covariance localization and inflation, the skill of the EnKBS is demonstrated in various important scientific problems. By integrating future observations, which reveal the underlying causal mechanisms for retrospective state updates, the EnKBS is used for Bayesian-based inference of causal relationships and their temporal influence range in a dyadic trigger-feedback model and the development of a causality-driven iterative learning algorithm that identifies the structure and recovers the hidden parameters of a nonlinear reduced-order model mimicking midlatitude atmospheric circulation. Notably, both tasks remain effective with an ensemble size of $O(10)$ under partial observations, suggesting that EnKBS can support the instantaneous discovery of high-dimensional complex systems over time.