A hybrid Method Based on Rational Legendre Physics Informed Neural Networks and Cuckoo Optimization Algorithm for Solving Nonlinear Inverse Partial Differential Equations

Articles in Press

Document Type : Research article

Authors

School of Mathematics and Computer Science, Damghan University, Damghan, Iran

10.22128/ansne.2026.3307.1213

Abstract

We develop an improved physics-informed neural network (PINN) framework for solving nonlinear inverse partial differential equations. Two separate network architectures are explored: one utilizing Legendre polynomials as activation functions and another employing rational Legendre polynomials. In the latter case, there is a crucial hyperparameter, $L$, that significantly impacts both performance and efficiency. To optimize this parameter, we employ the cuckoo optimization algorithm (COA), which fine-tunes $L$ based on the problem's characteristics. The proposed methods are tested on two benchmark problems, the Fisher equation and the Burgers--Fisher equation. The results highlight the effectiveness of both approaches, demonstrating superior accuracy in reconstructing unknown boundary conditions. All experiments were conducted in a Jupyter Notebook environment using PyTorch, confirming the potential of tailored activation functions and optimization techniques in physics-informed deep learning.

Keywords

Main Subjects

Analytical and Numerical Solutions for Nonlinear Equations

Articles in Press, Accepted Manuscript
Available Online from 26 July 2026

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History

  • Receive Date: 29 April 2026
  • Revise Date: 20 July 2026
  • Accept Date: 23 July 2026
  • Publish Date: 26 July 2026

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