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arXiv 2005.09622q-bio.QM
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从有限时间样本的生物学数据学习方程

Learning Equations from Biological Data with Limited Time Samples

John T. Nardini, John H. Lagergren, Andrea Hawkins-Daarud, Lee Curtin, Bethan Morris, Erica M. Rutter, Kristin R. Swanson, Kevin B. Flores

摘要:

方程学习方法为科学家在生物学数据的建模过程中提供了一个很有前途的工具。先前的方程学习研究已经证明,这些方法可以从丰富的数据集推断模型,然而,这些方法在生物学数据的共同挑战下的性能还没有得到彻底的探索。我们提出了一种方程学习方法,包括数据去噪,方程学习,模型选择和后处理步骤,从嘈杂的时空数据推断出一个动态系统模型。这种方法的性能进行了彻底的调查,在面对几个常见的挑战,即由生物学数据,稀疏的数据采样,大的噪声水平,和数据集之间的异质性。我们发现,这种方法可以准确地推断出正确的基本方程,并预测未观察到的系统动态时,从少量的时间样本的数据是在一个时间间隔内采样表现出线性和非线性动态。我们的研究结果表明,当使用信息数据集时,方程学习方法可用于生物学许多领域的模型发现和选择。在这项工作中,我们专注于多形性胶质母细胞瘤建模作为案例研究,以强调这些结果如何为基于数据驱动的建模的肿瘤侵袭预测提供信息。

英文摘要:

Equation learning methods present a promising tool to aid scientists in the modeling process for biological data. Previous equation learning studies have demonstrated that these methods can infer models from rich datasets, however, the performance of these methods in the presence of common challenges from biological data has not been thoroughly explored. We present an equation learning methodology comprised of data denoising, equation learning, model selection and post-processing steps that infers a dynamical systems model from noisy spatiotemporal data. The performance of this methodology is thoroughly investigated in the face of several common challenges presented by biological data, namely, sparse data sampling, large noise levels, and heterogeneity between datasets. We find that this methodology can accurately infer the correct underlying equation and predict unobserved system dynamics from a small number of time samples when the data is sampled over a time interval exhibiting both linear and nonlinear dynamics. Our findings suggest that equation learning methods can be used for model discovery and selection in many areas of biology when an informative dataset is used. We focus on glioblastoma multiforme modeling as a case study in this work to highlight how these results are informative for data-driven modeling-based tumor invasion predictions.

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