Algorithm for joint optimization of machine learning for upgrading a finite difference model

¹ Russian State Agrarian University – Moscow Timiryazev Agricultural Academy (RSAU – MTAA), Department of Physics, 127434, Timiryazevskaya st., 49, Moscow, Russian Federation
² Donetsk State University (DonSU), Department of Theoretical Physics and Nanotechnology, 283001 Universitetskaya st. 24, Donetsk, Russian Federation

^* Corresponding author: yulduz19.77@mail.ru

Abstract

Modernization of the finite element model is currently the basic tool for refining the numerical solution of modeling problems by adjusting the numerical response to the observed empirical behavior of the system. Recently, the modification of the model in some cases is carried out using the maximum likelihood method. Following this approach, the update problem can be transformed into a multiobjective optimization problem. Due to the non-trivial non-linear behavior of the desired objective functions, metaheuristic optimization algorithms are usually used to solve such an optimization problem. However, despite the fact that recently this method has proven itself quite well, nevertheless, there are two significant drawbacks that must be eliminated for the practical application of this method. Among which are the length of time spent on the calculation of the problem and the uncertainty associated with choosing the most optimal updated model among all Pareto optimal solutions. To circumvent these limitations, this paper proposes to apply a new joint algorithm that takes advantage of the joint relationship between two optimization algorithms, a machine learning method, and a statistical toolkit. As a result of the study, two main advantages of the newly proposed algorithm were revealed: it leads to a clear reduction in simulation time; and also allows you to make a reliable choice of the best updated model.