Prior Knowledge Informed Neural Network for Subsurface Flow Prediction

Data-driven deep learning has been widely applied to solve subsurface flow problems. However, it is difficult to achieve accurate prediction with pure data-driven methods, especially when there is only a small amount of valid data. Prior knowledge is pre-existent and comes from an independent source. The neural network can be informed by prior knowledge to improve algorithm performance even with limited and sparse data. In this study, prior knowledge informed neural network (PKINN) is proposed to predict subsurface flow. The prior knowledge, on the one hand, is embedded in the neural networks as integrated loss function to inform the training process of deep learning methods. On the other hand, it is used as part of input term of neural network to improve calculation accuracy. Subsurface flow models are built to verify the proposed PKINN model. The results show that the PKINN method can solve subsurface flow problems effectively.