  In recent years, Scientific Machine Learning (SciML) methods for solving
partial differential equations (PDEs) have gained increasing popularity. Within
such a paradigm, Physics-Informed Neural Networks (PINNs) are novel deep
learning frameworks for solving initial-boundary value problems involving
nonlinear PDEs. Recently, PINNs have shown promising results in several
application fields. Motivated by applications to gas filtration problems, here
we 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 the
efficacy of the PINN framework for solving such kind of problems. In
particular, we estimate an appropriate approximation error for some test
problems whose analytical solutions are fortunately known. The numerical
experiments discussed include two and three-dimensional spatial domains,
emphasizing the effectiveness of this approach in predicting accurate
solutions.
