Efficient Inverse Modeling of Flow Problems Using the Non-Intrusive Reduced Basis Two-Grid Method

Ensemble-based inverse modeling that employs high-fidelity (HF) models can be computationally prohibitive due to the need for repeated model simulation across a wide range of uncertain parameters. To address this limitation, we introduce a computationally efficient inverse modeling framework that incorporates the non-intrusive reduced basis (NIRB) two-grid method into the restart Ensemble Kalman Filter (rEnKF) approach. The NIRB technique facilitates the rapid reconstruction of HF solutions from coarse-grid models by using precomputed reduced basis functions and rectification matrices. This offline–online decomposition can greatly reduce computational costs not only during parameter estimation but also in the overall modeling process that includes training. We validate this framework using a 3D single-phase flow problem in a porous medium with a binary hydraulic conductivity field based on the SPE10 benchmark. The numerical examples demonstrate that the NIRB–rEnKF framework maintains estimation accuracy comparable to that of HF-rEnKF while achieving substantial improvements in computational performance. The approach proves particularly effective in settings where the amount of training data is limited but larger ensemble sizes are required to avoid filter inbreeding. Overall, this work offers a practical and scalable solution for ensemble-based inverse modeling at low computational cost in complex subsurface systems.