On the feasibility of an ensemble multi-fidelity neural network for fast data assimilation for subsurface flow in porous media

Uncertainty quantification (UQ) of the reservoir heterogeneity is essential to predict fluid flow behavior in subsurface formations accurately, and the task is often accomplished by integrating high-fidelity forward physics simulators with iterative data assimilation methods, and such workflows are usually computationally expensive due to the iterative nature and the prohibitive cost of physics simulations. In this work, we develop anew Ensemble Multi-Fidelity Neural Network (EMF-Net) to mitigate the efficiency bottleneck of UQ. EMF-Net directly infers the uncertain variables (e.g., permeability) via the sparse observation of the state variables (e.g., pressure). By leveraging the regression capability of deep neural networks, EMF-Net directly learns the nonlinear mapping from the innovation vector to the inferred update vector without the hypothesis of a linear mapping. At the training phase, high-fidelity data computed by a physics simulator (fh) and low-fidelity data computed by a forward proxy model (fl) are used to train the EMFNet at two different stages, respectively. At the inference phase, we first adopt the 1-stage EMF-Net to infer the update vector for the initial ensembles with a global tuning and then efficiently update the innovation vector by f l . As an option, we further refine the inference, via a 2-stage EMF-Net, which captures the locality and enhances consistency with the observation data. We demonstrate that EMF-Net can reach equivalent inference accuracy compared to classic data assimilation algorithms like ES-MDA, in addition to decreasing the CPU time. Therefore, the accuracy and efficiency make it an attractive alternative for scalable real-time history-matching tasks in field-scale subsurface engineering applications.