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The reaction-diffusion equation is one of the cornerstones equations inapplied science and engineering. In the present study, a deep neural networkhas been trained in order to predict the solution of the equation withdifferent coefficients using the numerical solution of this equation and theutility of deep learning. Analytical solution of the Reaction-Diffusionequation also has been conducted by taking advantage of the Danckwerts method.The accuracy of deep learning results was compared with the analyticalsolutions. In order to decrease the learning time and to find out similarequations solutions, such as pure diffusion and pure reaction, dimensionalanalysis technique has been performed. It was demonstrated that deep learningcan accurately estimate the Partial Differential Equations solutionin the caseof the reaction-diffusion equation with a constant coefficient.

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