Вісник № 02. Системний аналіз, управління та інформаційні технології
Постійне посилання колекціїhttps://repository.kpi.kharkov.ua/handle/KhPI-Press/55880
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Документ Using of multilayer neural networks for the solving systems of differential equations(Національний технічний університет "Харківський політехнічний інститут", 2021) Marchenko, Natalia Andriyivna; Sydorenko, Ganna Yurijivna; Rudenko, Roman OleksandrovychThe article considers the study of methods for numerical solution of systems of differential equations using neural networks. To achieve this goal, the following interdependent tasks were solved: an overview of industries that need to solve systems of differential equations, a s well as implemented a method of solving systems of differential equations using neural networks. It is shown that different types of systems of differential equations can be solved by a single method, which requires only the problem of loss function for optimization, which is directly created from differential equations and does not require solving equations for the highest derivative. The solution of differential equations’ system using a multilayer neural networks is the functions given in analytical form, which can be differentiated or integrated analytically. In the course of this work, an improved form of construction of a test solution of systems of differential equations was found, which satisfies the initial conditions for construction, but has less impact on the solution error at a distance from the initial conditions compared to the form of such solution. The way has also been found to modify the calculation of the loss function for cases when the solution process stops at the local minimum, which will be caused by the high dependence of the subsequent values of the functions on the accuracy of finding the previous values. Among the results, it can be noted that the solution of differential equations’ system using artificial neural networks may be more accurate than classical numerical methods for solving differential equations, but usually takes much longer to achieve similar results on small problems. The main advantage of using neural networks to solve differential equations` system is that the solution is in analytical form and can be found not only for individual values of parameters of equations, but also for a ll values of parameters in a limited range of values.