Investigation of the Predictive Capabilities of a Data-Driven Multilayer Model by the Example of the Duffing Oscillator

The article discusses modern requirements for methods of processing dynamic measurements in the framework of such areas as the Internet of Things, Cyber-Physical Systems, and Digital Twins. In the context of the need to reduce the processing time and complexity of the model, it is proposed to apply multilayer methods based on grid methods for constructing data-driven models including problems with unknown dynamic parameters of the system. The authors use this approach to solve the Duffing equation. In the course of solving the problem, the identification of the unknown dynamic parameter of the system is also carried out. As basic methods, universal iterative formulas for differential equations of the first order (various modifications of the Euler method, the Runge-Kutta method, and others) and the Störmer method for the second order equation are considered. The analysis of the quality of the constructed models is carried out. It has been found that multilayer models have sufficiently good predictive properties. The properties of different models allow to choose the appropriate model depending on the specific problem being solved. The simplicity of the multilayer models based on grid methods and the low cost of computations are noted as one of the most important advantages for modern approaches to processing dynamic measurements of the observed system and constructing predictive data-driven models.