Numerical simulation by Deep Learning for discrete nonlinear problems involving the anisotropic p(.)-Laplacian

In this paper, we establish the existence of a class of discrete nonlinear systems involving the anisotropic p⃗(⋅)-Laplacian operator using an optimization based approach. We then simulate the solutions by implementing a deep learning model. The numerical results demonstrate that the proposed method is stable and robust compared to conventional approaches such as the Newton–Krylov method.