Overall Research Project Description There have recently been many new developments in solving differential equations using data science techniques. See for example the "PINN" ("Physics Informed Neural Networks") method developed by Prof. Karniadakis at Brown University. Are these methods better than classical methods (finite element, finite difference, finite volume, or Runge Kutta methods) for solving differential equations? It could be that the new ``data science motivated'' methods are a transformative development since the methods are "embarrassingly vectorizable" (for GPU processing) and have anecdotally been shown to represent solutions using a minimum number of degrees of freedom. There are many test problems to try and compare classical methods to data science techniques, all ranging in level of difficulty.