Informed Reconstruction-Oriented Numerical Networks: A More Efficient Method for Solving Multiple Unknown Parameters of Manakov Equations

Abstract By simultaneously introducing a finite-difference-based numerical loss term and a clustering–reconstruction mechanism, we propose an enhanced physics-informed neural network named the informed reconstruction-oriented numerical network (IRON-Net) and subsequently apply it to the Manakov equations—a well-known two-component nonlinear physical model. Numerical experiments are conducted on a dataset containing eight analytical solutions with noise. The results indicate that, compared to conventional PINNs and other mainstream algorithms, IRON-Net demonstrates significant advantages in training accuracy, convergence rate, and robustness, achieving a stepwise improvement in the neural network’s ability to enforce physical constraints. Additional ablation experiments further confirm the necessity of the consistency constraint within IRON-Net. This study provides an effective approach for modeling and parameter identification in complex nonlinear optical systems as well as other nonlinear physical scenarios.