Feedforward Neural Network in MATLAB for One Dimensional Linear Convection Equation

In this research, a feedforward neural network in MATLAB is used to solve a one-dimensional linear convection equation, and its performance is compared to an analytical solution.By learning geographical and temporal patterns from data produced by the explicit first order upwind technique, we employ an ANN to approximate the temperature distribution.In MATLAB, the Levenberg-Marquardt algorithm is utilized as an optimization method.In order to illustrate the numerical solution of the convection equation and error function, surface and contour maps are also created.Additionally, a quantitative analysis of the prediction is conducted by comparing the precise answer with the predicted real values using the Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and R2 value.When compared to traditional numerical techniques, the results show that the ANN is an accurate and effective substitute for solving linear PDEs.