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

Fractional complex networks have significant advantages 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, under conditions of uncertain parameters and unknown topological structure, traditional methods struggle to accurately identify the parameters and topology jointly, which limits the practical application of such networks. To address this issue, this paper proposes a framework based on machine learning, which for the first time introduces three types of neural network models (Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Reservoir Computing (RC) into the parameter estimation and topological structure identification of fractional complex networks. By generating observed data based on the Caputo fractional derivative and the Adams-Bashforth-Moulton discretization method, and through the design of a reasonable loss function combined with the Adam optimizer, the network parameters and topological structure are iteratively solved. Numerical experiments show that LSTM, GRU, and RC all have high reliability, with RC having the best overall performance. This research provides a new method for solving inverse problems in fractional complex networks, and it remains valid for integer-order complex networks.