PDFP-enhanced physics-informed neural networks for solving higher-order PDEs: Application to engineering beam problems

  • Shahbaz Ahmad orcid

    Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan
  • Neha Zaman orcid

    Department of Mathematics, Government Post Graduate College Mansehra, Mansehra 21300, Pakistan
  • Muhammad Asif orcid

    Department of Mathematics, Government Post Graduate College Mansehra, Mansehra 21300, Pakistan
  • Muhammad Qasim orcid

    Government Degree College Havelian, Abbottabad 22010, Pakistan
  • Aaqib Hussain Shah orcid

    Department of Chemistry, Government Post Graduate College Mansehra, Mansehra 21300, Pakistan
  • Anam Shahzadi orcid

    Islamabad Model College for Girls, Islamabad 44000, Pakistan
  • Faizan Arshid orcid

    Department of Mathematics, Government Post Graduate College Mansehra, Mansehra 21300, Pakistan
  • Muhammad Israr orcid

    Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan

    Department of Mathematics, Government Post Graduate College Mansehra, Mansehra 21300, Pakistan
Article ID: 4125
DOI: https://doi.org/10.59400/mea4125
Keywords: quasi newton optimization, PDFP optimizer, neural network, PINNs, euler–bernoulli beam problem, timoshenko beam problem

Abstract

This study introduces a modern technique for solving beam equations on elastic foundations, applied to Euler–Bernoulli and Timoshenko beams based on the Winkler foundation. Conventional Physics-Informed Neural Networks (PINNs) have faced major challenges in handling large space-time domains, even when closed-form solutions exist. To address these challenges, we introduced a preconditioned PINNs loss function that incorporates prior knowledge from similar problems, thereby enhancing both productivity and accuracy. This novel method improves the generalization capability of PINNs in structural engineering, specifically for beam dynamics on elastic foundations. The effectiveness of the method is shown through numerical simulations on Euler–Bernoulli beams and extended domains for Timoshenko beams. Comparing with state-of-the-art PINNs shows that our method speeds up the convergence and precisely describes the behavior of the system, surpassing current strategies under the L2-norm metric. Besides, we examine the weight and weight loss plots, and present 3D visualizations of the best weight configurations. Further, we describe the superior performance of the proposed method. The present study explores the application of Preconditioned Devidon–Fletcher–Powell (PDFP)-enhanced Physics-Informed Neural Networks (PINNs) for solving higher-order partial differential equations, with particular emphasis on their implementation in engineering beam problems. It provides an overview of the new approach for addressing complex beam dynamics, including visualizations of the neural network architectures, PINNs convergence behavior, and representative solutions for the beam problems.

Published
2026-01-27
How to Cite
Ahmad, S., Zaman, N., Asif, M., Qasim, M., Shah, A. H., Shahzadi, A., Arshid, F., & Israr, M. (2026). PDFP-enhanced physics-informed neural networks for solving higher-order PDEs: Application to engineering beam problems. Mechanical Engineering Advances, 4(1). https://doi.org/10.59400/mea4125
Issue
Vol. 4 No. 1 (2026)
Section
Article

Copyright (c) 2026 Shahbaz Ahmad, Neha Zaman, Muhammad Asif, Muhammad Qasim, Aaqib Hussain Shah, Anam Shahzadi, Faizan Arshid, Muhammad Israr

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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