  In this paper, we compute numerical approximations of the minimal surfaces,
an essential type of Partial Differential Equation (PDE), in higher dimensions.
Classical methods cannot handle it in this case because of the Curse of
Dimensionality, where the computational cost of these methods increases
exponentially fast in response to higher problem dimensions, far beyond the
computing capacity of any modern supercomputers. Only in the past few years
have machine learning researchers been able to mitigate this problem. The
solution method chosen here is a model known as a Physics-Informed Neural
Network (PINN) which trains a deep neural network (DNN) to solve the minimal
surface PDE. It can be scaled up into higher dimensions and trained relatively
quickly even on a laptop with no GPU. Due to the inability to view the
high-dimension output, our data is presented as snippets of a higher-dimension
shape with enough fixed axes so that it is viewable with 3-D graphs. Not only
will the functionality of this method be tested, but we will also explore
potential limitations in the method's performance.
