A novel method, based on the combination of data assimilation and machine learning is introduced. The new hybrid approach is designed for a two-fold scope: (i) emulating hidden, possibly chaotic, dynamics and (ii) predicting their future states. The method consists in applying iteratively a data assimilation step, here an ensemble Kalman filter, and a neural network. Data assimilation is used to optimally combine a surrogate model with sparse noisy data. The output analysis is spatially complete and is used as a training set by the neural network to update the surrogate model. The two steps are then repeated iteratively. Numerical experiments have been carried out using the chaotic 40-variables Lorenz 96 model, proving both convergence and statistical skill of the proposed hybrid approach. The surrogate model shows short-term forecast skill up to two Lyapunov times, the retrieval of positive Lyapunov exponents as well as the more energetic frequencies of the power density spectrum. The sensitivity of the method to critical setup parameters is also presented: the forecast skill decreases smoothly with increased observational noise but drops abruptly if less than half of the model domain is observed. The successful synergy between data assimilation and machine learning, proven here with a low-dimensional system, encourages further investigation of such hybrids with more sophisticated dynamics.

介绍了一种基于数据同化和机器学习相结合的新方法。新的混合方法设计用于两个方面：（i）模拟隐藏的，可能是混沌的动力学，以及（ii）预测其未来状态。该方法包括迭代地应用数据同化步骤，这里是集成卡尔曼滤波器和神经网络。数据同化用于将替代模型与稀疏噪声数据最佳地组合在一起。输出分析在空间上是完整的，并且被神经网络用作训练集以更新代理模型。然后迭代地重复这两个步骤。使用混沌40变量Lorenz 96模型进行了数值实验，证明了所提出的混合方法的收敛性和统计能力。替代模型显示了最多两次李雅普诺夫时间的短期预测技能，正李雅普诺夫指数的检索以及功率密度谱的更活跃的频率。还介绍了该方法对关键设置参数的敏感性：随着观察噪声的增加，预测技能会平滑降低，但如果观察不到模型域的一半，则预测技能会突然下降。数据同化和机器学习之间的成功协同作用（已在此处使用低维系统进行了证明）鼓励进一步研究具有更复杂动态特性的此类混合动力。预测技巧会随着观察噪声的增加而平稳降低，但如果观察不到模型域的一半，则预测能力会突然下降。数据同化和机器学习之间的成功协同作用（已在此处使用低维系统进行了证明）鼓励进一步研究具有更复杂动态特性的此类混合动力。预测技巧会随着观察噪声的增加而平滑降低，但如果观察不到模型域的一半，则预测能力会突然下降。数据同化和机器学习之间的成功协同作用（已在此处使用低维系统进行了证明）鼓励进一步研究具有更复杂动态特性的此类混合动力。