On examining the predictive capabilities of two variants of the PINN in validating localized wave solutions in the generalized nonlinear Schrödinger equation

Thulasidharan, K and Sinthuja, N and Priya, NV and Senthilvelan, M (2024) On examining the predictive capabilities of two variants of the PINN in validating localized wave solutions in the generalized nonlinear Schrödinger equation. In: Communications in Theoretical Physics, 76 (11).

PDF Com_The_Phy_Vol_76_Iss_11_2024.pdf - Published Version Restricted to Registered users only Download (2MB) | Request a copy

Abstract

We introduce a novel neural network structure called strongly constrained theory-guided neural network (SCTgNN), to investigate the behaviour of the localized solutions of the generalized nonlinear Schrödinger (NLS) equation. This equation comprises four physically significant nonlinear evolution equations, namely, the NLS, Hirota, Lakshmanan-Porsezian-Daniel and fifth-order NLS equations. The generalized NLS equation demonstrates nonlinear effects up to quintic order, indicating rich and complex dynamics in various fields of physics. By combining concepts from the physics-informed neural network and theory-guided neural network (TgNN) models, the SCTgNN aims to enhance our understanding of complex phenomena, particularly within nonlinear systems that defy conventional patterns. To begin, we employ the TgNN method to predict the behaviour of localized waves, including solitons, rogue waves and breathers, within the generalized NLS equation. We then use the SCTgNN to predict the aforementioned localized solutions and calculate the mean square errors in both the SCTgNN and TgNN in predicting these three localized solutions. Our findings reveal that both models excel in understanding complex behaviour and provide predictions across a wide variety of situations. © 2024 Institute of Theoretical Physics CAS, Chinese Physical Society and IOP Publishing. All rights, including for text and data mining, AI training, and similar technologies, are reserved.

Item Type:	Journal Article
Publication:	Communications in Theoretical Physics
Publisher:	Institute of Physics
Additional Information:	The copyright for this article belongs to the publishers.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	30 Oct 2024 04:41
Last Modified:	30 Oct 2024 04:41
URI:	http://eprints.iisc.ac.in/id/eprint/86590

Actions (login required)

View Item