Filtering is a data assimilation technique that performs the sequential inference of dynamical systems states from noisy observations. Herein, we propose a machine learning-based ensemble conditional mean filter (ML-EnCMF) for tracking possibly high-dimensional non-Gaussian state models with nonlinear dynamics based on sparse observations. The proposed filtering method is developed based on the conditional expectation and numerically implemented using machine learning (ML) techniques combined with the ensemble method. The contribution of this work is twofold. First, we demonstrate that the ensembles assimilated using the ensemble conditional mean filter (EnCMF) provide an unbiased estimator of the Bayesian posterior mean, and their variance matches the expected conditional variance. Second, we implement the EnCMF using artificial neural networks, which have a significant advantage in representing nonlinear functions over high-dimensional domains such as the conditional mean. Finally, we demonstrate the effectiveness of the ML-EnCMF for tracking the states of Lorenz-63 and Lorenz-96 systems under the chaotic regime. Numerical results show that the ML-EnCMF outperforms the ensemble Kalman filter.
翻译:过滤是一种数据同化技术,它从噪音的观测中测得动态系统的顺序推论。 我们在此提出一个基于机器的学习混合式有条件平均过滤器(ML-EnCMF),用于跟踪可能具有高维的非高加索状态模型,其非线性动态基于稀少的观测。 拟议的过滤方法基于有条件的预期,并使用机体学习(ML)技术以及混合法进行数字化实施。 这项工作的贡献是双重的。 首先,我们证明使用混合式有条件平均过滤器(ENCMF)吸收的共聚体为Bayesian后方位平均值提供了公正的估测器,其差异与预期的有条件差异相符。 其次,我们使用人工线性网络实施EnCMF,这在代表高维(例如有条件平均值)的非线性功能方面有很大优势。 最后,我们展示了ML- EnCMF在跟踪混乱制度下的Lrenz-63和Lorepernz-96系统状态方面的效力。 Numericalal 结果表明,MFerma mass 将Me massimmal系统排出MLL-CMMMF。