Efficient Training of Deep-Learning-Based Surrogate Models for Subsurface Flow Simulation Using Multifidelity Data and Physics Constraints

Summary In the field of subsurface flow simulation, deep-learning-based surrogate modeling is shown as a promising approach to significantly reduce the computational cost associated with full-physics reservoir simulations. However, the successful construction of highly accurate deep-learning-based models often requires a large number of training simulations, which can be very time-consuming to generate by itself for large-scale systems. The incorporation of physics constraints during the training process was shown to be an effective approach to reduce the training cost and to improve model accuracy. However, it remains challenging to reimplement the physics constraints correctly for modeling training when it comes to reservoir models with complex physics or gridding methods. In this study, we propose a physics-constrained surrogate (PCS) model training approach for production optimization that integrates multifidelity training data, together with a new way of implementing the physics constraints that leverages an existing mature reservoir simulator. The proposed approach starts with model pretraining on a relatively large number of low-cost, low-fidelity training data, followed by model fine-tuning with a smaller number of high-fidelity training samples and the inclusion of physics constraints. The physics constraints are implemented by adding the residuals of discretized governing equations into the loss function. Training with multifidelity data and incorporating physics constraints allows for reduced reliance on high-fidelity data while enhancing physical consistency. Systematic comparison studies were performed for both 2D and 3D cases, and it was shown that the proposed approach can reduce the computational costs associated with training data generation by about 80%, while achieving a similar level of prediction accuracy of the surrogate model. In addition, under a small number of training simulations (i.e., 50 equivalent high-fidelity runs), our proposed PCS model with multifidelity data can reduce the prediction error by 90%, in comparison with the model trained with only high-fidelity data. Finally, the trained surrogate model was applied to a well-control optimization problem. In comparison with the use of full-order simulations, the total computational time can be reduced by 97.7%.