In this paper, we briefly outlined the physical principles underlying a physics-informed neural networks designed to solve partial differential equations [1]. The application of nonlinear Schrodinger equations to fiber lasers with a semiconductor optical amplifier is considered. And improved the neural network architecture and combined the PReLU activation function [2] (Parametric Rectified Linear Unit) and Latin hypercube sampling in the neural network model [3] to effectively approximate the soliton solution of the nonlinear Schrodinger equation [4] to reduce training time and improve model accuracy.
List of literature
1. Raissi M., Perdikaris P., Karniadakis G.E. Physics-informed deep learning (part i): Data-driven solutions of nonlinear partial differential equations. arXiv preprint arXiv: 1711. 2017. p.~10561.
2. He K., Zhang X., Ren S., et al. Delving deep into rectifiers: Surpassing human-level performance on imagenet classification~//Proceedings of the IEEE international conference on computer vision. 2015. p.~1026--1034.
3. Keramat M., Kielbasa R. Latin hypercube sampling Monte Carlo estimation of average quality index for integrated circuits. Analog Integrated circuits and signal processing. 1997. №~14, p.~131--142.
4. Matusevich O. V., Trofimov V. A. Numerical method for finding 3D solitons of the nonlinear Schrodinger equation in the axially symmetric case. Journal of Computational Mathematics and Mathematical Physics. 2009. Vol. 49. No.~11. 1988-2000.