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<p>Fractional complex networks have substantial practical potential in real-world modeling, such as in biological neural networks and communication systems, due to their ability to describe the long-term memory effect and high degree of freedom of the system. However, when the network parameters and topological structure are unknown, traditional methods struggle to jointly identify the parameters and topology, which limits the practical application of such networks. To address this issue, we propose a machine learning (ML) framework that applies Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Reservoir Computing (RC) to parameter and topology identification in fractional complex networks. By generating observed data from the Caputo fractional complex network, using the Adams–Bashforth-Moulton scheme, and by constructing a loss function optimized with the Adam algorithm, the network parameters and topological structure are iteratively estimated. Numerical experiments show that LSTM, GRU, and RC all achieve high identification reliability, and RC shows more stable convergence and lower prediction loss under the considered experimental settings. This research provides a method for solving inverse problems in fractional complex networks, and it remains valid for integer-order complex networks.</p>

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Machine Learning-Based Parameter Estimation and Topology Identification of Uncertain Fractional-Order Complex Networks

  • 期刊论文

  • 发表日期：

    2026年5月22日

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  • Ce Liang,
  • Weiyuan Ma

摘要

Fractional complex networks have substantial practical potential in real-world modeling, such as in biological neural networks and communication systems, due to their ability to describe the long-term memory effect and high degree of freedom of the system. However, when the network parameters and topological structure are unknown, traditional methods struggle to jointly identify the parameters and topology, which limits the practical application of such networks. To address this issue, we propose a machine learning (ML) framework that applies Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Reservoir Computing (RC) to parameter and topology identification in fractional complex networks. By generating observed data from the Caputo fractional complex network, using the Adams–Bashforth-Moulton scheme, and by constructing a loss function optimized with the Adam algorithm, the network parameters and topological structure are iteratively estimated. Numerical experiments show that LSTM, GRU, and RC all achieve high identification reliability, and RC shows more stable convergence and lower prediction loss under the considered experimental settings. This research provides a method for solving inverse problems in fractional complex networks, and it remains valid for integer-order complex networks.