Abstract.

In this paper, we commence by providing a succinct overview of the mechanics behind Physics-Informed Neural Networks (PINNs) tailored for resolving partial differential equations (PDEs), along with an introduction to certain nonlinear Schr¨ odinger equations perti nent to applications in semiconductor optical amplifier fiber lasers. Subsequently, we introduce an innovative architecture for PINNs, which incorporates an adaptive activation function and Latin Hypercube Sampling, aimed at the efficient approximation of soliton solutions to non linear Schr¨ odinger equations. A series of numerical examples are presented to illustrate the straightforwardness and effectiveness of our proposed approach.

Keywords:

nonlinear Schr¨ odinger equation, soliton, machine learning, physics-informed neural networks.