The dynamics of a physical system is usually determined by solving a differential equation. It normally proceeds by reducing the differential equation to a familiar form with a known compact solution using suitable coordinate transformations. In non-trivial cases, however, finding the appropriate transformation is difficult and numerical methods are used. A number of algorithms (e.g., Runge-Kutta, finite difference, etc) are available for calculating the solution accurately and efficiently. However, these methods are sequential and require much memory space and time, as a result, have great computational cost. Here, we demonstrate an Artificial Neural Network approach to finding solutions of Parabolic Partial Differential Equation (PPDE). We use an unsupervised feed-forward Neural Network to solve. We illustrate the method by solving a variety of PPDE model problems including Burger’s equation that is the one-dimensional quasi-linear PPDE.