Parameter identification of dynamical systems based on short-term prediction by the generalized cell mapping method with deep learning

Dynamic analysis based on observed data has emerged as a prominent research focus due to the challenges associated with obtaining mathematical models that rely on strong assumptions. An innovative approach termed the improved generalized cell mapping method with deep learning (IGCM-DL) for parameter identification in dynamical systems is presented in this paper, leveraging short-term prediction utilizing experimental data. The proposed method integrates a parallel neural network and Markov theory to extract and learn the underlying dynamics of the system. By establishing a comprehensive mapping relationship among system parameters, initial conditions, and responses, the proposed method enables accurate prediction of system responses over arbitrary time durations. The optimal system parameters are achieved through systematic traversal of the parameter domain. Extensive numerical simulations and tests are conducted on both a typical Duffing-Van der Pol system and the Lorenz system to validate the performance. Results demonstrate that the IGCM-DL method facilitates precise parameter identification, accurately capturing the short-term evolution law of systems including periodic, limit cycle, and chaotic behaviors.