PHYSICS INFORMED NEURAL NETWORK WITH MULTIDIMENSIONAL WEIGHT CONNECTIONS FOR DIFFERENTIAL EQUATIONS

Kabul Khudaybergenov; Farrux Baxritdinov; Kudaybergenov Jabbarbergen

Авторы

Kabul Khudaybergenov Kimyo International University in Tashkent
Farrux Baxritdinov Kimyo International University in Tashkent
Kudaybergenov Jabbarbergen Tashkent University of Information Technologies Nukus branch named after Muhammad Al-Khwarizmi

Ключевые слова:

Physics-informed neural network, Differential equation, weight connection, numerical solution

Аннотация

Recently, Physics-Informed Neural Network (PINN) models has shown as a promising approach for solving various types physical problems which include differential equations. However, from numerical point of view, PINN models have some issues related to local minima problems when solving with minimal initial conditions. In this work, we propose a new robust PINN model which employes neural network with multidimensional weight connections to solve this issue. The proposed PINN model shows advantages over classical neural network model which is not capable of extrapolation and does not rely on large datasets. We first investigate the numeral solution of differential equation with initial conditions with a classical neural network and the PINN with neural network with multidimensional weight connections. Computational experiments show the advantage of proposed PINN model over existing classical methods which does not demand a large number of data points and also some sophisticated mathematical methods that work linear computations.

Библиографические ссылки

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