Cuckoo Search Optimized Fractional Physics-Informed Neural Networks for Fourth-Order Time-Fractional Partial Differential Equations

Ali Alkhathlan, Faris Kateb, Tauqeer Ahmad, Muhammad Sulaiman and Mohammed Abdullah Salman

Journal of Mathematics, 2026, vol. 2026, 1-21

Abstract: Time-fractional fourth-order partial differential equations (PDEs) are typically important in the modeling of complex physical systems that have long-memory effects and high-order transverse spatial interaction. The paper presents a new hybrid method, called the Cuckoo Search–optimized fractional physics-informed neural network (fPINN-CS), that, to the best of our knowledge, combines evolutionary metaheuristic optimization with fPINNs to auto-optimize architecture and hyperparameter choices to time-fractional high-order PDEs. The given approach uses Cuckoo Search with Lévy flights, nest selection, and solution rejection strategies that allow the proposed approach to explore the solution space efficiently worldwide, thus, avoiding the necessity of heuristic-based tuning. The framework incorporates fractional operators in the physics-informed learning paradigm, which guarantees precise management of memory dynamics. Numerous numerical benchmark studies of the proposed approach on time-fractional fourth-order subdiffusion equation, Kuramoto–Sivashinsky equation, and Cahn–Hilliard equation have shown that the proposed approach predicts significantly more accurately, is more stable, and converges more robustly than traditional PINN-based algorithms. The findings above indicate that fPINN-CS has a potential of being a trusted and automatic solver of complex fractional PDE systems.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:3727060

DOI: 10.1155/jom/3727060

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