We develop an advanced physics-informed neural network (PINN) framework to simultaneously address the forward modeling of nonlinear wave dynamics and the inverse reconstruction of complex potentials in the P7-symmetric derivative nonlinear Schr & ouml;dinger (DNLS) equation. In the forward regime, the enhanced multi-layer architecture accurately captures diverse bright, multihump, and structurally enriched soliton states supported by Scarf-II and harmonic-Hermite-Gaussian P7-symmetric potentials, achieving near-perfect agreement with analytical profiles. In the inverse regime, the proposed method reliably infers multiple real-valued parameters and functional forms of complex P7 potentials from sparsely sampled solution data, demonstrating strong resilience to noise and data scarcity. By incorporating a modified PINN strategy (mPINN), we further accomplish the data-driven discovery of potential landscapes associated with the P7-DNLS model. A systematic assessment of key hyperparameters, including activation functions, network depth, and collocation strategies, reveals their essential roles in enhancing approximation fidelity and training robustness. Numerical results confirm that our framework delivers a unified, accurate, and computationally efficient paradigm for both forward prediction and inverse identification of nonlinear P7-symmetric dispersive systems. This work provides a novel pathway for leveraging deep learning to explore non-Hermitian physics, with promising extensions to higher-order, fractional, and multi-dimensional P7-symmetric models.

Publication:

PHYSICA D-NONLINEAR PHENOMENA

http://dx.doi.org/10.1016/j.physd.2026.135290

Author:

Chen, Yong

Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Peoples R China

Liu, Liwei

Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Peoples R China

Tao, Wei

Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Peoples R China

Yan, Zhenya(corresponding author)

Zhongyuan Univ Technol, Sch Math & Informat Sci, Zhengzhou 450007, Peoples R China

Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Math Sci, Beijing 100190, Peoples R China

Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

Email address:zyyan@mmrc.iss.ac.cn