Investigation of the Predictive Capabilities of a Data-Driven Multilayer Neuromorphic Model by the Example of the Duffing Oscillator
Abstract
The transition to Industry 4.0 highlights areas of research that require a qualitative description of a complex system, for example, a cyber-physical one, in the form of an adaptive dynamic model since the systems themselves are subject to change over time under various, sometimes unknown factors. In this paper, we test a new method for refining a mathematical model and building a medium-term forecast based on processing dynamic measurements. In the context of the need to reduce processing time and model complexity, we use our multilayer models based on mesh methods applied to a variable-length time interval. The methods we have developed are an alternative way of constructing approximate functional solutions of differential equations. In this paper, this approach is used to solve the Duffing equation with a variable parameter. The basic methods are universal iterative formulas for first-order differential equations in the form of various modifications of the Euler method and Störmer's method for second-order equations. The article presents the results of calculating the execution time of iterations and their comparative analysis, as well as a preliminary assessment of the presence of significant differences in the applied schemes using the Friedman test for a sample with unchanged parameters and pair wise comparison using the Wilcoxon test to determine the nature of the difference in values. We performed the calculations using the Wolfram Mathematica package and analyzed them using the built-in functions of the Excel package. The data obtained help to optimize the use of schemes for practical purposes, thus, our comparative study of the properties of different models allows us to choose the most suitable model depending on the specific problem being solved. On the basis of these data, in the future, it is possible to develop a system that automatically selects the most acceptable method for solving the problem determined by the input data.
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