Deep learning for parameter identification of nonlinear dynamical system driven by fractional Brownian motion

Abstract This paper presents a deep learning-based parameter identifier capable of jointly identifying all parameters of a nonlinear dynamical system driven with fractional Brownian motion (FBM). Firstly, a new parameter identifier (TBNN) is constructed by combining the advantages of transformer in dealing with long-term dependence and bidirectional long short-term memory (BiLSTM) in extracting local features. Next, FBM is introduced as the random effect in the nonlinear dynamical system, and three examples are provided to simulate the established system. Finally, the TBNN identifier is used to identify the parameters of the three systems individually and compares with the PENN identifier to verify its effectiveness. The results demonstrate that the proposed TBNN identifier can identify all parameters of the nonlinear dynamical system more quickly and accurately. Additionally, three advantages of the TBNN identifier are discussed, including the stability of parameter identification results, the rationality of sample size selection, and the advantages of TBNN network construction.