Modelling One Dimensional Heat Equation Using Feed Forward Neural Networks: A Comparative Study with Analytical Solutions

This research paper presents the use of a feedforward neural network to solve heat conduction equation and compares its performance with the exact solution.We use an ANN to approximate heat distribution by learning spatial and temporal patterns from data generated by the explicit finite difference method.Levenberg-Marquardt algorithm (LMA) is used as optimization algorithm in MATLAB.Also surface and contour plots are developed which are used to demonstrate numerical solution of the heat equation and error function.In addition, the prediction is quantitative analyzed by comparison of the predicted real values and the exact solution by Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and R value.The results illustrate that the ANN is an accurate and efficient alternative for solving ODEs when compared to traditional numerical methods.