# Learning partial differential equations for biological transport models from noisy spatiotemporal data

## TL;DR

This paper presents a novel neural network-based denoising approach for accurately learning biological PDE models from noisy spatiotemporal data, outperforming traditional methods.

## Contribution

It introduces an ANN-based denoising method that improves PDE discovery accuracy from noisy biological data, surpassing existing denoising techniques.

## Key findings

- ANN denoising outperforms finite differences and splines.
- The method accurately recovers PDE models from noisy data.
- Effective on biological transport PDEs like Fisher-KPP.

## Abstract

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.