A novel approach to modeling incommensurate fractional order systems using fractional neural networks

Kumar, Meshach and Mehta, Utkal V. and Cirrincione, Giansalvo (2024) A novel approach to modeling incommensurate fractional order systems using fractional neural networks. Mathematics, 12 (1). NA. ISSN 2227-7390

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Abstract

This research explores the application of the Riemann–Liouville fractional sigmoid, briefly RLFσ, activation function in modeling the chaotic dynamics of Chua’s circuit through Multilayer Perceptron (MLP) architecture. Grounded in the context of chaotic systems, the study aims to address the limitations of conventional activation functions in capturing complex relationships within datasets. Employing a structured approach, the methods involve training MLP models with various activation functions, including RLFσ, sigmoid, swish, and proportional Caputo derivative PCσ, and subjecting them to rigorous comparative analyses. The main findings reveal that the proposed RLFσ consistently outperforms traditional counterparts, exhibiting superior accuracy, reduced Mean Squared Error, and faster convergence. Notably, the study extends its investigation to scenarios with reduced dataset sizes and network parameter reductions, demonstrating the robustness and adaptability of RLFσ. The results, supported by convergence curves and CPU training times, underscore the efficiency and practical applicability of the proposed activation function. This research contributes a new perspective on enhancing neural network architectures for system modeling, showcasing the potential of RLFσ in real-world applications.

Item Type:	Journal Article
Subjects:	T Technology > TK Electrical engineering. Electronics Nuclear engineering > Robotics and Automation
Divisions:	School of Information Technology, Engineering, Mathematics and Physics (STEMP)
Depositing User:	Utkal Mehta
Date Deposited:	01 Feb 2024 23:27
Last Modified:	30 Jan 2025 00:04
URI:	https://repository.usp.ac.fj/id/eprint/14397

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