Bayesian polynomial neural networks and polynomial neural ordinary differential equations.

IF 3.8 2区生物学 Q1 BIOCHEMICAL RESEARCH METHODS PLoS Computational Biology Pub Date : 2024-10-10 eCollection Date: 2024-10-01 DOI:10.1371/journal.pcbi.1012414

Colby Fronk, Jaewoong Yun, Prashant Singh, Linda Petzold

引用次数: 0

Abstract

Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. However, these methods provide point estimates for the model parameters and are currently unable to accommodate noisy data. We address this challenge by developing and validating the following Bayesian inference methods: the Laplace approximation, Markov Chain Monte Carlo (MCMC) sampling methods, and variational inference. We have found the Laplace approximation to be the best method for this class of problems. Our work can be easily extended to the broader class of symbolic neural networks to which the polynomial neural network belongs.

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贝叶斯多项式神经网络和多项式神经常微分方程。

多项式神经网络符号回归和多项式神经常微分方程（ODEs）是近期用于许多科学和工程问题方程复原的两种强大方法。然而，这些方法提供的是模型参数的点估计，目前无法适应噪声数据。我们通过开发和验证以下贝叶斯推理方法来应对这一挑战：拉普拉斯近似、马尔可夫链蒙特卡罗（MCMC）抽样方法和变分推理。我们发现拉普拉斯近似法是解决这类问题的最佳方法。我们的工作很容易扩展到多项式神经网络所属的更广泛的符号神经网络类别。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

PLoS Computational Biology BIOCHEMICAL RESEARCH METHODS-MATHEMATICAL & COMPUTATIONAL BIOLOGY

CiteScore

7.10

自引率

4.70%

发文量

820

审稿时长

2.5 months

期刊介绍： PLOS Computational Biology features works of exceptional significance that further our understanding of living systems at all scales—from molecules and cells, to patient populations and ecosystems—through the application of computational methods. Readers include life and computational scientists, who can take the important findings presented here to the next level of discovery. Research articles must be declared as belonging to a relevant section. More information about the sections can be found in the submission guidelines. Research articles should model aspects of biological systems, demonstrate both methodological and scientific novelty, and provide profound new biological insights. Generally, reliability and significance of biological discovery through computation should be validated and enriched by experimental studies. Inclusion of experimental validation is not required for publication, but should be referenced where possible. Inclusion of experimental validation of a modest biological discovery through computation does not render a manuscript suitable for PLOS Computational Biology. Research articles specifically designated as Methods papers should describe outstanding methods of exceptional importance that have been shown, or have the promise to provide new biological insights. The method must already be widely adopted, or have the promise of wide adoption by a broad community of users. Enhancements to existing published methods will only be considered if those enhancements bring exceptional new capabilities.