A recurrent neural network framework with an adaptive training strategy for long-time predictive modeling of nonlinear dynamical systems. (18th August 2021)

• Record Type: Journal Article
• Authors: Li, Shanwu; Yang, Yongchao
• Is Part Of: Journal of sound and vibration. Volume 506(2021)
• Publication Date: 2021-08-18
• Subjects: Nonlinear dynamical system -- Data-driven model -- Long-time prediction -- Recurrent neural network -- Duffing system -- Attractor; Sound -- Periodicals; Vibration -- Periodicals; Son -- Périodiques; Vibration -- Périodiques; Sound; Vibration; Periodicals; Electronic journals; 620.205
• DOI: 10.1016/j.jsv.2021.116167
• Languages: English
• ISSNs: 0022-460X

Abstract

Highlights: A novel method for data-driven predictive modeling of nonlinear dynamics is proposed. This method includes a recurrent neural network framework and a training strategy. The strategy facilitates the training of recurrent neural network. The demonstration on various systems shows accuracy and robustness of the method. Abstract: Long-time prediction of future states has been challenging in data-driven modeling of nonlinear dynamical systems as the prediction error accumulates over the prediction horizon. One of the potential reasons is the lack of robustness for the data-driven model. In this study we present a recurrent neural network (RNN) framework with an adaptive training strategy to model nonlinear dynamical systems from data for long-time prediction of future states. Specifically, we exploit the recurrence of network to improve the model robustness by explicitly incorporating the multi-step prediction with error accumulation into model training. Furthermore, we introduce an adaptive training strategy, where the prediction horizon gradually increases from a small value to facilitate the RNN training. We demonstrate the proposed approach on a family of Duffing oscillators, including autonomous and non-autonomous systems with various attractors, and discuss its advantages and limitations.