ArticleProceedings. Mathematical, physical, and engineering sciences2020
Learning partial differential equations for biological transport models from noisy spatio-temporal data.
Article in Proceedings. Mathematical, physical, and engineering sciences, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 21 papers.
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21 citing papers in PubMed.
- Enhancing generalizability of model discovery across parameter space with multi-experiment equation learning for biological systems.PLoS computational biology · 2026Article
- Advances in surrogate modeling for biological agent-based simulations: trends, challenges, and future prospects.Journal of mathematical biology · 2025Review
- Inference and prediction for stochastic models of biological populations undergoing migration and proliferation.Journal of the Royal Society, Interface · 2025Review
- Mathematical modeling of multicellular tumor spheroids quantifies inter-patient and intra-tumor heterogeneity.NPJ systems biology and applications · 2025Article
- Data-driven model discovery and model selection for noisy biological systems.PLoS computational biology · 2025Article
- Weak-form inference for hybrid dynamical systems in ecology.Journal of the Royal Society, Interface · 2024Article
- Guidelines for mechanistic modeling and analysis in cardiovascular research.American journal of physiology. Heart and circulatory physiology · 2024Review
- Learning dynamical systems from data: An introduction to physics-guided deep learning.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
- From biological data to oscillator models using SINDy.iScience · 2024Article
- Verifiable biology.Journal of the Royal Society, Interface · 2023Review
- Learning mean-field equations from particle data using WSINDy.Physica D. Nonlinear phenomena · 2022Article
- Computationally efficient mechanism discovery for cell invasion with uncertainty quantification.PLoS computational biology · 2022Article
- A theoretical framework to analyse the flow of particles in a dynamical system with stochastic transition rates and site capacities.Royal Society open science · 2022Article
- WEAK SINDY FOR PARTIAL DIFFERENTIAL EQUATIONS.Journal of computational physics · 2021Article
- Bayesian uncertainty quantification for data-driven equation learning.Proceedings. Mathematical, physical, and engineering sciences · 2021Article
- Learning differential equation models from stochastic agent-based model simulations.Journal of the Royal Society, Interface · 2021Article
- Detection and characterization of chemotaxis without cell tracking.Journal of the Royal Society, Interface · 2021Article
- WEAK SINDy: GALERKIN-BASED DATA-DRIVEN MODEL SELECTION.Multiscale modeling & simulation : a SIAM interdisciplinary journal · 2021Article
- Development of a hybrid model for a partially known intracellular signaling pathway through correction term estimation and neural network modeling.PLoS computational biology · 2020Article
- Biologically-informed neural networks guide mechanistic modeling from sparse experimental data.PLoS computational biology · 2020Article
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5 authors.
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Abstract
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.
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