PINN Based on Domain Adaptation for Solving Fornberg–Whitham-Type Equations

Shirong Li (), Huan Guo, Maliyamuguli Maimaiti and Shaoyong Lai
Additional contact information
Shirong Li: College of Mathematics and Statistics, Kashi University, Kashi 844008, China
Huan Guo: College of Mathematics and Statistics, Kashi University, Kashi 844008, China
Maliyamuguli Maimaiti: College of Mathematics and Statistics, Kashi University, Kashi 844008, China
Shaoyong Lai: School of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China

Mathematics, 2025, vol. 13, issue 22, 1-18

Abstract: The Fornberg–Whitham equation, which contains high-order nonlinear derivatives, is widely recognized as a prominent model for describing shallow water dynamics. We explore physics-informed neural networks (PINsN) in conjunction with transfer learning technology to investigate numerical solutions for the FW equation. The proposed domain adaptation in transfer learning for PINN transforms the complex problem defined over the entire spatiotemporal domain into simpler problems defined over smaller subdomains. Training a neural network on these subdomains provides extra supervised learning data, effectively addressing optimization challenges associated with PINNs. Consequently, it enables the resolution of anisotropic and long-term predictive issues in these types of equations. Moreover, it enhances prediction accuracy and accelerates loss convergence by circumventing local optima in the specified scenarios. The method efficiently handles both forward and inverse FW equation problems, excelling in cost-effective accurate predictions for inverse problems. The efficiency and accuracy of our proposed approaches are demonstrated through examples and results.

Keywords: physics-informed neural networks; Fornberg–Whitham equation; transfer learning; inverse problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/22/3607/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/22/3607/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:22:p:3607-:d:1791678

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().