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

• Published in: Journal of computational physics Vol. 509; p. 113059
• Main Authors: Zhang, Xin-Lei, Zhang, Lei, He, Guowei
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.07.2024
• Subjects: Data assimilation; Ensemble Kalman method; Field inversion; Machine learning; Parallel implementation; Field inversion; Parallel implementation; Ensemble Kalman method; Machine learning; Data assimilation
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2024.113059

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 ensemble-based 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. •The analysis scheme of the ensemble Kalman method is parallelized based on non-overlapping domain decomposition.•The total variation regularization is utilized to alleviate the discontinuity near subdomain interfaces.•The method enables field inversion with large data amounts by partitioning observation data regionally.•The approach reduces computational costs significantly with satisfactory inversion accuracy and ease of implementation.