Anchored Physics-Informed Neural Network for Two-Phase Flow Simulation in Heterogeneous Porous Media

In this study, we propose a tensorization-anchoring strategy based on adaptive architectures to accelerate the computation of Enriched Physics-Informed Neural Networks (EPINN) for two-phase flow simulations. Specifically, we design an adaptive tensorization mechanism for the adjacency matrix embedding, the activation function, and the skip-gated connection in EPINN, which collectively expand the neural network's (NN) parameter space for learning more generalized patterns. Moreover, we developed an anchoring strategy by establishing Anchors-EPINN (An-EPINN). By detaching tensorization parameters from the computational graph and anchoring weighted nodes to fixed positions, the NN can benefit from tensorized fusion effects while reducing high-dimensional matrix calculations during forward and backward propagation, thereby enhancing simulation efficiency. This approach reduces execution time by 31.47% in homogeneous cases and 27.91% in heterogeneous cases, while maintaining higher computational accuracy.