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

Journal of Data Science

article

Anirban Chakraborty¹  Matthias Katzfuss¹ 

[1] Department of Statistics, Texas A&M University, 3143 TAMU, College Station

关键词: basis functions;    data assimilation;    hierarchical Vecchia approximation;    Lorenz model;    unscented Kalman filter;   

DOI  :  10.6339/22-JDS1071

学科分类：土木及结构工程学

来源: JDS

【 摘 要 】

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.

【 授权许可】

CC BY