Parallel ensemble Kalman method with total variation regularization for large-scale field inversion

Xinlei Zhang

doi:10.1016/j.jcp.2024.113059

2024-07-01

PRE

Xinlei Zhang

Lei Zhang

Guowei He *

DOI：10.1016/j.jcp.2024.113059

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摘要

En 中文

Field inversion is often encountered in data -driven computational modeling to infer latent spatial- varying parameters from available observations. The ensemble Kalman method is emerging as a useful tool for solving field inversion problems due to its derivative -free merits. However, the method is computationally prohibitive for large-scale field inversion with high -dimensional observation data, which necessitates developing a practical efficient implementation strategy. In this work, we propose a parallel implementation of the ensemble Kalman method with total variation regularization for large-scale field inversion problems. It is achieved by partitioning the computational domain into non -overlapping subdomains and performing local ensemble Kalman updates at each subdomain parallelly. In doing so, the computational complexity of the ensemblebased inversion method is significantly reduced to the level of local subdomains. Further, the total variation regularization is employed to smoothen the physical field over the entire domain, which can reduce the inference discrepancy caused by missing covariances near subdomain interfaces. The capability of the proposed method is demonstrated in three field inversion problems with increasing complexity, i.e., the diffusion problem, the scalar transport problem and the Reynolds averaged Navier-Stokes closure problem. The numerical results show that the proposed method can significantly improve computational efficiency with satisfactory inference accuracy.

Keyword:

Ensemble Kalman method

Parallel implementation

Field inversion

Data assimilation

Machine learning