Электронный каталог

Статья

Belicheva, D.M.
Using NeuralPDE.jl to Solve Differential Equations / D.M.Belicheva, D.S.Kulyabov, [a.o.]. – Text : electronic // Discrete and Continuous Models and Applied Computational Science. – 2025. – Vol. 33, No. 3. – P. 284-298. – URL: https://doi.org/10.22363/2658-4670-2025-33-3-284-298. – Bibliogr.: 21.

This paper describes the application of physics-informed neural network (PINN) for solving partialderivative equations. Physics Informed Neural Network is a type of deep learning that takes into account physicallaws to solve physical equations more efficiently compared to classical methods. The solution of partial derivativeequations (PDEs) is of most interest, since numerical methods and classical deep learning methods are inefficientand too difficult to tune in cases when the complex physics of the process needs to be taken into account. Theadvantage of PINN is that it minimizes a loss function during training, which takes into account the constraints ofthe system and th e laws of the domain. In this paper, we consider the solution of ordinary differential equations(ODEs) and PDEs using PINN, and then compare the efficiency and accuracy of this solution method comparedto classical methods. The solution is implemented in the Julia programming language. We use NeuralPDE.jl,a package containing methods for solving equations in partial derivatives using physics-based neural networks.The classical method for solving PDEs is implemented through the DifferentialEquations.jl library. As a result,a comparative analysis of the considered solution methods for ODEs and PDEs has been performed, and anevaluation of their performance and accuracy has been obtained. In this paper we have demonstrated the basiccapabilities of the NeuralPDE.jl package and its efficiency in comparison with numerical methods



Спец.(статьи,препринты) = С 17 д - Численное решение дифференциальных и интегральных уравнений. Разностные методы
Спец.(статьи,препринты) = С 325.1а - Нейронные сети и клеточные автоматы
ОИЯИ = ОИЯИ (JINR)2025