  Differential equations are used in a wide variety of disciplines, describing
the complex behavior of the physical world. Analytic solutions to these
equations are often difficult to solve for, limiting our current ability to
solve complex differential equations and necessitating sophisticated numerical
methods to approximate solutions. Trained neural networks act as universal
function approximators, able to numerically solve differential equations in a
novel way. In this work, methods and applications of neural network algorithms
for numerically solving differential equations are explored, with an emphasis
on varying loss functions and biological applications. Variations on
traditional loss function and training parameters show promise in making neural
network-aided solutions more efficient, allowing for the investigation of more
complex equations governing biological principles.
