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In recent years, Scientific Machine Learning (SciML) methods for solvingpartial differential equations (PDEs) have gained increasing popularity. Withinsuch a paradigm, Physics-Informed Neural Networks (PINNs) are novel deeplearning frameworks for solving initial-boundary value problems involvingnonlinear PDEs. Recently, PINNs have shown promising results in severalapplication fields. Motivated by applications to gas filtration problems, herewe present and evaluate a PINN-based approach to predict solutions to$strongly\,\,degenerate\,\,parabolic\,\,problems\,\,with\,\,asymptotic\,\,structure\,\,of\,\,Laplacian\,\,type$.To the best of our knowledge, this is one of the first papers demonstrating theefficacy of the PINN framework for solving such kind of problems. Inparticular, we estimate an appropriate approximation error for some testproblems whose analytical solutions are fortunately known. The numericalexperiments discussed include two and three-dimensional spatial domains,emphasizing the effectiveness of this approach in predicting accuratesolutions.

A physics-informed deep learning approach for solving strongly degenerate parabolic problems