A novel Transformer-Enhanced PINN approach to the Fokas–Lenells equation: Forward and inverse problems

This work introduces Transformer-Enhanced Physics-Informed Neural Networks (Tra-PINNs), a novel architecture for simulating diverse soliton solutions of the Fokas–Lenells (FL) equation. Replacing fully connected layers in Physics-Informed Neural Networks (PINNs) with attention mechanisms, Tra-PINNs effectively capture multi-scale temporal dependencies along the t-dimension in time-evolving partial differential equation (PDE) systems. Comprehensive numerical simulations demonstrate Tra-PINNs’ capability to accurately model bright/dark single-soliton and two soliton solutions with order-of-magnitude error reduction, where standard PINNs exhibit convergence failures under identical configurations. Crucially, Tra-PINNs maintain parametric invariance-simulating perturbed bright two soliton regimes without architectural adjustments-revealing nonlinear interactions while confirming exceptional robustness. Finally, we establish a data-parameter correlation framework, inferring two critical FL equation parameters and quantitatively linking dataset heterogeneity to solution fidelity. Our approach advances soliton simulation through temporally adaptive learning, offering new tools for nonlinear wave dynamics.