论文标题
使用集合Kalman过滤器对状态和动态的在线学习
Online learning of both state and dynamics using ensemble Kalman filters
论文作者
论文摘要
最新的机器学习进展使观察到的物理系统作为替代模型的动力学重建已成为尖锐的。为了处理该努力中的部分和嘈杂的观察，可以在贝叶斯数据同化框架中使用替代模型的机器学习表示。但是，这些方法需要考虑长时间序列的观察数据，该数据旨在将所有内容融合在一起。本文研究了在线学习动态和状态的可能性，即随时更新其估计值，特别是当获得新的观察结果时。该估计基于使用相当简单的替代模型和状态增强的相当简单的表示，基于算法的集合卡尔曼过滤器（ENKF）家族。我们考虑通过（i）在线学习动力学的含义，（i）本地ENKF和（iii）迭代ENKF，我们在每种情况下讨论的问题和算法解决方案中讨论。然后，我们使用一维，一尺度和两尺度的混沌Lorenz模型在数值上证明了这些方法的效率并评估了这些方法的准确性。
The reconstruction of the dynamics of an observed physical system as a surrogate model has been brought to the fore by recent advances in machine learning. To deal with partial and noisy observations in that endeavor, machine learning representations of the surrogate model can be used within a Bayesian data assimilation framework. However, these approaches require to consider long time series of observational data, meant to be assimilated all together. This paper investigates the possibility to learn both the dynamics and the state online, i.e. to update their estimates at any time, in particular when new observations are acquired. The estimation is based on the ensemble Kalman filter (EnKF) family of algorithms using a rather simple representation for the surrogate model and state augmentation. We consider the implication of learning dynamics online through (i) a global EnKF, (i) a local EnKF and (iii) an iterative EnKF and we discuss in each case issues and algorithmic solutions. We then demonstrate numerically the efficiency and assess the accuracy of these methods using one-dimensional, one-scale and two-scale chaotic Lorenz models.
