A deep learning PINN-LSTM fusion framework for solving ordinary differential equations from real-life systems

Shahul, Mohamed Ashik; Gunasekar, Tharmalingam; SANTRA, SHYAM SUNDAR; Baleanu, Dumitru; Yildirim, Yakup

doi:10.22124/jmm.2026.32516.2949

A deep learning PINN-LSTM fusion framework for solving ordinary differential equations from real-life systems

Articles in Press

Document Type : Research Article

Authors

¹ Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R\&D Institute of Science and Technology, Avadi, Chennai, India

² Khusigang, Sahapur, Bhangamora

³ Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon.

⁴ Department of Computer Engineering, Biruni University, Istanbul–34010, Turkey

10.22124/jmm.2026.32516.2949

Abstract

This article presents a comparative study of Physics Informed Neural Networks (PINNs), Long Short Term Memory (LSTM) networks and a novel Fusion of PINNs and LSTM for solving ordinary differential equations (ODEs) arising in real world problems. After brief preliminaries on PINNs and LSTM networks, we formulate PINN and LSTM frameworks and apply each to two benchmark systems: A Religious growth population problem and Kuramoto’s two oscillator problem. We then introduce an integration strategy that fuses PINN’s physics constrained learning with LSTM’s sequential modeling to improve stability and accuracy. Extensive numerical experiments and error analyses demonstrate that the proposed fusion architecture consistently outperforms standalone PINN and LSTM models in accuracy and robustness across the two problems. The results indicate the fusion approach as a promising direction for enhanced data efficient and physically consistent solutions of complex dynamical systems.

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