Solving the Reaction-Diffusion equation based on analytical methods and deep learning algorithm; the Case study of sulfate attack to concrete

TL;DR

This paper combines analytical methods and deep learning to solve the reaction-diffusion equation, demonstrating that deep learning can accurately estimate solutions with constant coefficients, validated against analytical solutions.

Contribution

It introduces a hybrid approach using analytical solutions and deep learning to efficiently solve reaction-diffusion equations with constant coefficients.

Findings

Deep learning accurately predicts reaction-diffusion solutions.

Analytical solutions were obtained using Danckwerts method.

Dimensional analysis reduces learning time and identifies similar solutions.

Abstract

The reaction-diffusion equation is one of the cornerstones equations in applied science and engineering. In the present study, a deep neural network has been trained in order to predict the solution of the equation with different coefficients using the numerical solution of this equation and the utility of deep learning. Analytical solution of the Reaction-Diffusion equation also has been conducted by taking advantage of the Danckwerts method. The accuracy of deep learning results was compared with the analytical solutions. In order to decrease the learning time and to find out similar equations solutions, such as pure diffusion and pure reaction, dimensional analysis technique has been performed. It was demonstrated that deep learning can accurately estimate the Partial Differential Equations solutionin the case of the reaction-diffusion equation with a constant coefficient.