Exploring data driven soliton and rogue waves in PT symmetric and spatio-temporal potentials using PINN and SC-PINN methods
Anand R. Manikandan K. Serikbayev N.
March 2025Springer Science and Business Media Deutschland GmbH
European Physical Journal Plus
2025#140Issue 3
In this study, we present a deep learning (DL) framework for solving the nonlinear Schrödinger equation with PT-symmetric potentials using strongly constrained physics-informed neural networks (SC-PINNs). We focus on three types of physically compelling potentials, namely PT-symmetric rational, Jacobian-periodic, and spatio-temporal dependent. SC-PINNs extend the standard physics-informed neural networks (PINNs) by incorporating compound derivative information into the soft constraints, along with an adaptive weight mechanism to accelerate loss function convergence. This enhancement significantly improves the training efficiency compared to standard PINNs. We employ SC-PINNs to approximate soliton and rogue wave solutions of the system under investigation. Additionally, we uncover the impact of various factors on the neural network’s performance, including five different nonlinear activation functions: ReLU, sigmoid, sech, tanh, and sine. Our results reveal that the SC-PINNs method achieves faster convergence and lower errors compared to traditional PINNs. Notably, when using the sine activation function for the three distinct potentials mentioned above, SC-PINNs reduced errors to the order of 10-7, 10-6, and 10-4, effectively capturing complex physical features for highly accurate predictions. Furthermore, we analyze the effect of PT-symmetric potential parameters on the obtained approximated solutions. The results demonstrate that our DL model successfully approximates soliton and rogue wave solutions of the considered system with high accuracy, outperforming traditional DL algorithms.
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Centre for Computational Modeling, Chennai Institute of Technology, Tamil Nadu, Chennai, 600069, India
Center for Nonlinear and Complex Networks, SRM TRP Engineering College, Tamil Nadu, Tiruchirappalli, 621105, India
Center for Research, SRM Institute of Science and Technology - Tiruchirappalli, Tamil Nadu, Tiruchirappalli, 621105, India
Department of General and Theoretical Physics, L. N. Gumilyov Eurasian National University, Astana, 010008, Kazakhstan
Centre for Computational Modeling
Center for Nonlinear and Complex Networks
Center for Research
Department of General and Theoretical Physics
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