Supplementary material from "Learning partial differential equations for biological transport models from noisy spatio-temporal data"
Posted on 2020-02-18 - 10:15
We investigate methods for learning partial differential equation (PDE) models from spatio-temporal 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 analyse the performance in using previous methods to denoise data for the task of discovering the governing system of 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–Kolmogorov–Petrovsky–Piskunov (Fisher–KPP) and nonlinear Fisher–KPP equations. We show that the ANN methodology outperforms previous denoising methods, including finite differences and both local and global polynomial regression splines, in the ability to accurately approximate partial derivatives and learn the correct PDE model.
CITE THIS COLLECTION
DataCiteDataCite
3 Biotech3 Biotech
3D Printing in Medicine3D Printing in Medicine
3D Research3D Research
3D-Printed Materials and Systems3D-Printed Materials and Systems
4OR4OR
AAPG BulletinAAPG Bulletin
AAPS OpenAAPS Open
AAPS PharmSciTechAAPS PharmSciTech
Abhandlungen aus dem Mathematischen Seminar der Universität HamburgAbhandlungen aus dem Mathematischen Seminar der Universität Hamburg
ABI Technik (German)ABI Technik (German)
Academic MedicineAcademic Medicine
Academic PediatricsAcademic Pediatrics
Academic PsychiatryAcademic Psychiatry
Academic QuestionsAcademic Questions
Academy of Management DiscoveriesAcademy of Management Discoveries
Academy of Management JournalAcademy of Management Journal
Academy of Management Learning and EducationAcademy of Management Learning and Education
Academy of Management PerspectivesAcademy of Management Perspectives
Academy of Management ProceedingsAcademy of Management Proceedings
Academy of Management ReviewAcademy of Management Review
Lagergren, John H.; Nardini, John T.; Michael Lavigne, G.; Rutter, Erica M.; Flores, Kevin B. (2020). Supplementary material from "Learning partial differential equations for biological transport models from noisy spatio-temporal data". The Royal Society. Collection. https://doi.org/10.6084/m9.figshare.c.4860342.v1