Multi-Distributed Sampling Method to Optimize Physical-Informed Neural Networks for Solving Optical Solitons

Abstract Optical solitons, as self-sustaining waveforms in a nonlinear medium where dispersion and nonlinear effects are balanced, have key applications in ultrafast laser systems and optical communications. Physics-informed neural networks (PINN) provide a new way to solve the nonlinear Schrödinger equation describing the soliton evolution by fusing data-driven and physical constraints. However, the grid point sampling strategy of traditional PINN suffers from high computational complexity and unstable gradient flow, which makes it difficult to capture the physical details efficiently. In this paper, we propose a residual-based adaptive multi-distribution (RAMD) sampling method to optimize the PINN training process by dynamically constructing a multi-modal loss distribution. With a 50% reduction in the number of grid points, RAMD significantly reduces the relative error of PINN and, in particular, optimizes the solution error of the (2+1) Ginzburg–Landau equation from 4.55% to 1.98%. RAMD breaks through the lack of physical constraints in the purely data-driven model by the innovative combination of multi-modal distribution modeling and autonomous sampling control for the design of all-optical communication devices. RAMD provides a high-precision numerical simulation tool for the design of all-optical communication devices, optimization of nonlinear laser devices, and other studies.