论文标题
通过合并数据同化，机器学习和期望 - 最大化来推断混乱动力学的推断
Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization
论文作者
论文摘要
（i）（i）可以实际获得的部分和嘈杂的观察结果，（ii）需要从长时间的数据中学习，以及（iiii）动力学的不稳定性质，从（i）局部和嘈杂的观察结果受到了（i）局部和嘈杂的观察，从而阻碍了高维混沌动力学（例如地球物理流）的重建，诸如地球物理流的观察结果（i）局部和嘈杂的观察结果受到了阻碍。为了从长期序列的观察结果中得出这种推论，有人建议以多种方式将数据同化和机器学习结合在一起。我们展示了如何使用预期最大化和协调下降来从贝叶斯的角度统一这些方法。在此过程中，模型，状态轨迹和模型误差统计量将共同估算。讨论了这些方法的实现和近似值。最后，我们在两个相关的低阶混沌模型上，在数值上成功地测试了该方法，具有明显的可识别性。
The reconstruction from observations of high-dimensional chaotic dynamics such as geophysical flows is hampered by (i) the partial and noisy observations that can realistically be obtained, (ii) the need to learn from long time series of data, and (iii) the unstable nature of the dynamics. To achieve such inference from the observations over long time series, it has been suggested to combine data assimilation and machine learning in several ways. We show how to unify these approaches from a Bayesian perspective using expectation-maximization and coordinate descents. In doing so, the model, the state trajectory and model error statistics are estimated all together. Implementations and approximations of these methods are discussed. Finally, we numerically and successfully test the approach on two relevant low-order chaotic models with distinct identifiability.
