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An efficient zeroing neural network for solving time-varying nonlinear equations

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Abstract

Defining efficient families of recurrent neural networks (RNN) models for solving time-varying nonlinear equations is an interesting research topic in applied mathematics. Accordingly, one of the underlying elements in designing RNN is the use of efficient nonlinear activation functions. The role of the activation function is to bring out an output from a set of input values that are supplied into a node. Our goal is to define new family of activation functions consisting of a fixed gain parameter and a functional part. Corresponding zeroing neural networks (ZNN) is defined, termed as varying-parameter improved zeroing neural network (VPIZNN), and applied to solving time-varying nonlinear equations. Compared with previous ZNN models, the new VPIZNN models reach an accelerated finite-time convergence due to the new time-varying activation function which is embedded into the VPIZNN design. Theoretical results and numerical experiments are presented to demonstrate the superiority of the novel VPIZNN formula. The capability of the proposed VPIZNN models are demonstrated in studying and solving the Van der Pol equation and finding the root \(\root m \of {a(t)}\).

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All data generated or analyzed during this study are included in this submitted article (and its supplementary information files).

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Funding

Department of Computational and Data Sciences, Indian Institute of Science, Bangalore, 560012, India. “Savas Parastatidis” named scholarship granted by the Bodossaki Foundation. Ratikanta Behera has received research grant from the Indian Institute of Science, Bangalore, India. Predrag Stanimirović is supported by the Science Fund of the Republic of Serbia, (No. 7750185, Quantitative Automata Models: Fundamental Problems and Applications - QUAM). Predrag Stanimirović gratefully acknowledge support from the Ministry of Education, Science and Technological Development, Republic of Serbia, grant no. 451-03-47/2023-01/200124. Dimitrios Gerontitis stood by financial support of the “Savas Parastatidis” named scholarship granted by the Bodossaki Foundation.

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Authors and Affiliations

  1. Department of Computational and Data Sciences, Indian Institute of Science, Bangalore, 560012, India

    Ratikanta Behera

  2. Department of Information and Electronic Engineering, International Hellenic University, Thessaloniki, Greece

    Dimitris Gerontitis

  3. Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000, Niš, Serbia

    Predrag Stanimirović

  4. Department of Economics, National and Kapodistrian University of Athens, Athens, Greece

    Vasilios Katsikis

  5. School of Information Engineering, Yangzhou University, Yangzhou, China

    Yang Shi

  6. School of Business, Jiangnan University, Wuxi, China

    Xinwei Cao

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  1. Ratikanta Behera
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  2. Dimitris Gerontitis
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  4. Vasilios Katsikis
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  5. Yang Shi
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  6. Xinwei Cao
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Correspondence to Dimitris Gerontitis.

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Behera, R., Gerontitis, D., Stanimirović, P. et al. An efficient zeroing neural network for solving time-varying nonlinear equations. Neural Comput & Applic 35, 17537–17554 (2023). https://doi.org/10.1007/s00521-023-08621-x

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