Learning partial differential equations for biological transport models from noisy spatiotemporal data
| Autor: | John T. Nardini, Erica M. Rutter, Kevin B. Flores, John H. Lagergren, G. Michael Lavigne |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Polynomial regression
0303 health sciences Partial differential equation Artificial neural network Estimation theory Computer science General Mathematics Noise reduction General Engineering Finite difference General Physics and Astronomy Dynamical Systems (math.DS) 01 natural sciences 010104 statistics & probability 03 medical and health sciences Nonlinear system FOS: Mathematics Partial derivative 0101 mathematics Mathematics - Dynamical Systems Algorithm Research Article 030304 developmental biology |
| Zdroj: | Proc Math Phys Eng Sci |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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