Learning partial differential equations for biological transport models from noisy spatio-temporal data
Learning partial differential equations for biological transport models from noisy spatio-temporal data
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DOI：
10.1098/rspa.2019.0800
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发表时间：
2020-02-26
影响因子：
3.5
通讯作者：
Flores, Kevin B.
中科院分区：
文献类型：
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作者：
Lagergren, John H.;Nardini, John T.;Flores, Kevin B.
我们研究了在生物学真实水平和噪声形式下从时空数据学习偏微分方程（PDE）模型的方法。从数据中学习偏微分方程的最新进展是使用稀疏回归从一组去噪数据中选择候选项，包括近似偏导数。我们分析了使用以前的方法对数据进行去噪以发现偏微分方程的控制系统的任务的性能。我们还开发了一种新颖的方法，使用人工神经网络（ANN）对数据进行去噪并近似偏导数。我们在生物传输的三种 PDE 模型上测试了该方法，即平流扩散、经典 Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) 和非线性 Fisher-KPP 方程。我们表明，ANN 方法在精确逼近偏导数和学习正确的 PDE 模型的能力方面优于以前的去噪方法，包括有限差分以及局部和全局多项式回归样条。
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.