Fractional Lotka-Volterra Parameters Estimation Using a Deep Convolutional Neural Network

Hadian, Amir Hosein; Biranvand, Nader; Partovi, Mohammad Taghi

doi:10.22034/jmor.2024.717828

Fractional Lotka-Volterra Parameters Estimation Using a Deep Convolutional Neural Network

Document Type : Original Article

Authors

Amir Hosein Hadian ¹

Nader Biranvand ²

Mohammad Taghi Partovi ³

¹ School of Computer Science, Institute for Research in Fundamental Science (IPM), Tehran, Iran

² Faculty of Sciences, Imam Ali University, Tehran, Iran

³ Department of Science and Technology Studies, AJA Command and Staff University, Tehran, Iran.

10.22034/jmor.2024.717828

Abstract

In the last decade, fractional calculus has attracted much attention and various fractional models have been developed by researchers. While the numerical simulation of fractional dynamics is very important to study, the parameter recovery of these models has many industrial and scientific applications and there is an overlook to this area in the literature on fractional dynamics. On the other hand, recently, artificial intelligence and deep learning methods have solved most of the challenges of dynamical system parameter recovery and the obtained results in the literature show the outstanding performance of these methods in comparison with other state-of-the-art numerical methods. In this paper, a deep convolutional neural network architecture which is named 'Deep-Inference', is utilized for the problem of parameter recovery of fractional Lotka-Volterra equations. This network is trained on the simulated behavior of the fractional Lotka-Volterra equation that is obtained by fractional Adams-Bashforth-Moulton. The obtained results illustrate the robust and high-precision performance of the proposed algorithm.

Keywords

Lotka-Volterra equations

Deep neural networks

Parameter estimation

Fractional calculus