High-Dimensional Nonlinear Spatio-Temporal Filtering by Compressing Hierarchical Sparse Cholesky Factors

Anirban Chakraborty, M. Katzfuss
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引用次数: 1

Abstract

Spatio-temporal filtering is a common and challenging task in many environmental applications, where the evolution is often nonlinear and the dimension of the spatial state may be very high. We propose a scalable filtering approach based on a hierarchical sparse Cholesky representation of the filtering covariance matrix. At each time point, we compress the sparse Cholesky factor into a dense matrix with a small number of columns. After applying the evolution to each of these columns, we decompress to obtain a hierarchical sparse Cholesky factor of the forecast covariance, which can then be updated based on newly available data. We illustrate the Cholesky evolution via an equivalent representation in terms of spatial basis functions. We also demonstrate the advantage of our method in numerical comparisons, including using a high-dimensional and nonlinear Lorenz model.
压缩分层稀疏Cholesky因子的高维非线性时空滤波
在许多环境应用中,时空滤波是一项常见且具有挑战性的任务,其中演化通常是非线性的,并且空间状态的维数可能非常高。我们提出了一种基于滤波协方差矩阵的分层稀疏Cholesky表示的可扩展滤波方法。在每个时间点,我们将稀疏的Cholesky因子压缩成具有少量列的密集矩阵。在对这些列中的每一列应用进化后,我们解压缩以获得预测协方差的分层稀疏Cholesky因子,然后可以根据新的可用数据更新该因子。我们通过空间基函数的等价表示来说明Cholesky演化。我们还证明了我们的方法在数值比较中的优势,包括使用高维和非线性洛伦兹模型。
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