title: Ð Ð°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¼ÐµÑÐ¾Ð´Ð° ÑÐµÑÐµÐ½Ð¸Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ Ð² ÑÐ°ÑÑÐ½ÑÑ Ð¿ÑÐ¾Ð¸Ð·Ð²Ð¾Ð´Ð½ÑÑ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð³ÐµÐ½ÐµÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Development of an automatic method for solving partial differential equations based on genetic programming
Creators: name: ÐÑÐ¸ÑÐ¸Ð½Ð°, ÐÐ»Ð¸Ð·Ð°Ð²ÐµÑÐ°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2022
Subjects: Ð³ÐµÐ½ÐµÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
ÑÐ¸Ð¼Ð²Ð¾Ð»ÑÐ½Ð°Ñ ÑÐµÐ³ÑÐµÑÑÐ¸Ñ
Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½ÑÐµ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ
ÑÐ¸Ð¼Ð²Ð¾Ð»ÑÐ½Ð¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ
genetic programming
symbolic regression
differential equations
symbolic solution

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description: The aim of this work is development of algorithm, solving partial differential equations, based on the genetic programming method. The developed algorithm should give a solution to the problem in symbolic form. The algorithm was tested on four elliptic equations with various right-hand sides and boundary conditions. It is shown that this method solves well with differential equations with rectangular boundaries. Convergence graphs for all equations are constructed. There are also illustrations of surfaces constructed according to the obtained equations. They completely coincide with the analytical solutions. The length of the functions generated by the method is studied depending on the equation. The dependence of the running time of the algorithm on the length of the solution was found: the longer the solution, the longer the program runs. An experiment was also conducted, for which other parameters of the algorithm were taken and the results were compared. Conclusions were drawn about the running time of programs with different parameters and about the relationship between the average error between runs with various parameters. As the main conclusion, was expressed that the algorithm developed in the framework of this work can give good results with elliptic equations with rectangular boundaries. For other equations, it is required to change the consideration of boundary conditions in the algorithm in order to obtain better results.