Soliton Solutions of Some Ocean Waves Supported by Physics Informed Neural Network Method

Abstract

In this study, we aim to obtain numerical results of the modified Benjamin-Bona-Mahony equation, Ostrovsky-Benjamin-Bona- Mahony equation, and Mikhailov-Novikov-Wang equation via the physics-informed neural networks (PINN) method. The equations are modeled for shallow and long water waves, as well as fundamental and phenomenal models in ocean engineering. According to the implementation, we obtained the PINN solutions of kink, bright, multi-soliton (two-soliton), and mixed dark-bright soliton solutions. According to the inference from the obtained results, we achieved good results in some cases compared to other approximate solution methods in the literature. However, it was also observed that the best possible results could not be obtained in cases where the soliton type was intricate and layered. While the results were obtained, the number of hidden layers and the number of neural networks in the layers also varied. These results are shown in tables. Since it is known that the aforementioned models are not solved by the PINN method, we anticipate that the study will lead to other studies in the field of ocean engineering.

Received: 11 December 2023 | Revised: 1 April 2024 | Accepted: 8 May 2024

Conflicts of Interest

The authors declare that they have no conflicts of interest to this work.

Data Availability Statement

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Author Contribution Statement

Ismail Onder: Conceptualization, Methodology, Software, Formal analysis. Mustafa Bayram: Validation, Investigation, Resources, Data curation. Abdulkadir Sahiner: Writing - original draft, Project administration. Aydin Secer: Writing - review & editing, Visualization, Supervision.