Continuous-Time State-Space Neural Network and Its Application in Modeling of Forced-Vibration Systems

Rapid advances in machine learning make it possible to formulate surrogate models for complex forced-vibration systems using neural networks. Recently, the continuous-time state-space neural network (CSNN) has shown great potential and has been drawing growing attention from the community. In this paper, we propose a generalized CSNN model for various forced-vibration systems. The CSNN model comprises two sets of independent neural networks aimed to compute the state derivative and system response, respectively. Both neural networks adopt linear and nonlinear layers in parallel, aimed to enhance the CSNN model with the capability to recognize the linear and nonlinear behaviors of systems. Additionally, the bias options in the CSNN model are all turned off to improve the stability of the model in the long-term time-series forecast. Integration on the state derivative is executed using the explicit 4th-order Runge-Kutta method. An illustrative example is provided in this paper, demonstrating that the CSNN model can achieve high performance and training efficiency with a few hyper-parameters.