Modeling of unsteady oscillations and thermal conductivity processes in a layer using deep machine learning technologies


Аuthors

Son P. T.

Le Quy Don Technical University, 236 Hoang Quoc Viet, Ha Noi, Viet Nam

e-mail: sonphantungk49@gmail.com

Abstract

Physically informed machine learning is a new, promising approach to solving various problems in mathematical physics, often those that cannot be solved by other methods or require significant expenditure of both human and machine time. Machine learning today is already a fairly developed and rapidly developing branch of applied mathematics. Machine learning methods and algorithms make it possible to successfully solve numerous pressing problems in a wide variety of industries, production technologies, economics and finance, e-commerce, medicine, construction, transport, etc. It should be noted that until just the last few years, deep machine learning was used almost exclusively in applied tasks based on the comparison of input and output data. Deep machine learning methods ignored the tasks of modeling physic-mechanical, chemical, biological and other processes, the mathematical models of which are systems of equations of mathematical physics, supplemented by boundary, initial conditions and other mathematical relations. These tasks are extremely important because they act as the foundation on which various applied industries rely.
The purpose of this work is to reveal the possibilities of applying deep machine learning methods to solving non-stationary problems of mechanics and thermal conductivity. The paper considers the processes of nonstationary oscillations and thermal conductivity in an elastic layer of constant thickness. Closed mathematical statements of the corresponding problems are given. It should be noted that these tasks act as model tasks. They are quite simple. Their solution can be obtained using analytical methods. The construction of solutions to these problems using deep machine learning methods is an initial step towards the development of new promising algorithms for solving various problems of mechanics of solids.
The paper provides solutions to the tasks set using analytical and numerical methods. The analytical approach to the solution is based on the method of separating variables. The numerical solution algorithm is built using deep machine learning technologies. A comparison of analytical and numerical results is carried out, confirming the prospects of applying the proposed methods to solving unsteady problems of solid mechanics.

Keywords:

elastic layer, thermal conductivity, unsteady oscillations, wave processes, physically informed neural networks, deep machine learning, variable separation method, gradient descent method, adam algorithm

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