  We investigate methods for learning partial differential equation (PDE)
models from spatiotemporal data under biologically realistic levels and forms
of noise. Recent progress in learning PDEs from data have used sparse
regression to select candidate terms from a denoised set of data, including
approximated partial derivatives. We analyze the performance in utilizing
previous methods to denoise data for the task of discovering the governing
system of partial differential equations (PDEs). We also develop a novel
methodology that uses artificial neural networks (ANNs) to denoise data and
approximate partial derivatives. We test the methodology on three PDE models
for biological transport, i.e., the advection-diffusion, classical Fisher-KPP,
and nonlinear Fisher-KPP equations. We show that the ANN methodology
outperforms previous denoising methods, including finite differences and
polynomial regression splines, in the ability to accurately approximate partial
derivatives and learn the correct PDE model.
