The line rogue wave solutions of the nonlocal Davey–Stewartson I equation with PT symmetry based on the improved physics-informed neural network.

The article focuses on employing an improved physics-informed neural network (PINN) algorithm to generate data-driven nonlinear wave solutions to the nonlocal Davey–Stewartson (DS) I equation with parity-time (PT) symmetry. By embedding both the PT symmetry and the nonlocal DS I model into the loss function and assigning distinct weights to its components, the improved PINN method addresses challenges posed by the equation’s high-dimensional coupled system and multi-output neural network requirements. The study successfully reproduces complex nonlinear waveforms—including line breather, kink-shaped, and W-shaped line rogue waves—with higher accuracy compared to the original PINN algorithm. These results demonstrate the feasibility of the improved PINN approach for investigating complex nonlinear waves in high-dimensional PT symmetric models.