Physics-informed radial basis function neural network for efficiently modeling oil–water two-phase Darcy flow

Physics-informed neural networks (PINNs) improve the accuracy and generalization ability of prediction by introducing physical constraints in the training process. As a model combining physical laws and deep learning, it has attracted wide attention. However, the training cost of PINNs is high, especially for the simulation of more complex two-phase Darcy flow. In this study, a physics-informed radial basis function neural network (PIRBFNN) is proposed to simulate two-phase Darcy flow of oil and water efficiently. Specifically, in each time step, oil phase and water phase equations are discretized based on the finite volume method, and then, the physics-informed loss is constructed according to the residual of their coupling equations, and the pressure is approximated by RBFNN. Based on the obtained pressure, another physics-informed loss is constructed according to the residual of discrete water phase equation and the water saturation is approximated by another RBFNN. For boundary conditions, we use “hard constraints” to speed up the training of PIRBFNN. The straightforward structure of PIRBFNN also contributes to an efficient training process. In addition, we have simply proved the ability of RBFNN to fit continuous functions. Finally, the experimental results also verify the computational efficiency of PIRBFNN. Compared with physics-informed convolutional neural network, the training time of PIRBFNN is reduced by more than three times.