Solving the Reaction-Diffusion equation based on analytical methods and deep learning algorithm; the Case study of sulfate attack to concrete
This work addresses computational modeling challenges in engineering, specifically for sulfate attack in concrete, but is incremental as it applies existing deep learning techniques to a known equation.
The study tackled solving the reaction-diffusion equation by combining deep learning with analytical methods, demonstrating that deep learning can accurately estimate solutions with constant coefficients, achieving high accuracy as validated against analytical results.
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.