Abstract
Recent advancements in deep learning have significantly improved solving complex computational physics problems. This paper presents Physics-Informed Neural Networks (PINNs) with a spatially-dependent diffusion function to model two-phase flow in porous media , explicitly addressing the Buckley-Leverett problem. The study analyzes the PINNs using different approaches, including diffusion term and modification flux function to convex hull, employing both Multi-Layer Perceptron (MLP) and Attention-based neural network architectures . In addition, we investigate the application of the PINNs for laboratory experimental data by assessing the performance of PINNs in capturing the saturation front dynamics. Our results indicate that while the attention-based model achieves slightly higher accuracy, it is significantly time-consuming. In contrast, the MLP is the more efficient in terms of training time with a speedup in the range of 7 − 13 . A sensitivity analysis on the constant diffusion coefficient shows that PINNs can approximately capture the pattern of the saturation front. We have found that adapting the spatial-dependent diffusion function provided better accuracy with the experimental data compared to using a constant diffusion coefficient .