Neural network-based numerical analysis of some convection-diffusion-based initial boundary-value problems

In this paper, we present a computational analysis of data-driven solutions of the convection–diffusion–reaction equation using Physics Informed Neural Networks (PINNs). PINNs enforce laws of physics when solving non-linear partial differential equations that govern physical dynamics. The PINN technique for solving boundary value problems in partial differential equations is presented as an alternative to the available numerical techniques. Three model initial-boundary value problems are implemented through MATLAB using the presented technique. The computed numerical solutions of these model problems are compared with the actual solution to observe the accuracy of the numerical implementation. It is noted that the predicted solution in the case of these model problems through PINNs is in strong agreement with the corresponding exact solution. The analysis of the presented algorithm is performed to observe what changes in the accuracy of the solution when the number of neurons and the number of layers working within the neural network structure are altered. Moreover, the impact of the number of training data points and collocation points on the model’s accuracy is also presented to develop a better understanding of the algorithm. It is observed that the presented method is capable of efficiently computing numerical solutions of boundary value problems in partial differential equations and has the potential to solve a large number of related problems that arise in engineering physics.