Data-driven learning of differential equations: combining data and model uncertainty
Data-driven learning of differential equations: combining data and model uncertainty
复制标题
数据驱动的微分方程学习：结合数据和模型不确定性
DOI：
10.1007/s40314-022-02180-y
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发表时间：
2023
影响因子：
2.6
通讯作者：
Glasner, Karl
中科院分区：
文献类型：
--
作者：
Glasner, Karl
Data-driven discovery of differential equations relies on estimating model parameters using information about a solution that is often incomplete and corrupted by noise. Moreover, the sizes of the uncertainties in the model and data are usually unknown as well. This paper develops a likelihood-type cost function which incorporates both sources of uncertainty and provides a theoretically justified way of optimizing the balance between them. This approach accommodates missing information about model solutions, allows for considerable noise in the data, and is demonstrated to provide estimates which are often superior to regression methods currently used for model discovery and calibration. Practical implementation and optimization strategies are discussed both for systems of ordinary differential and partial differential equations. Numerical experiments using synthetic data are performed for a variety of test problems, including those exhibiting chaotic or complex spatiotemporal behavior.
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影响因子：
2.6
作者：
Glasner, Karl
通讯作者：
Glasner, Karl
DOI：
10.48550/arxiv.1311.7602
发表时间：
2013
期刊：
--
影响因子：
--
作者：
Croft W
通讯作者：
Croft W
DOI：
10.1073/pnas.1517384113
发表时间：
2016-04-12
影响因子：
11.1
作者：
Brunton, Steven L.;Proctor, Joshua L.;Kutz, J. Nathan
通讯作者：
Kutz, J. Nathan
数据驱动的发现
DOI：
--
发表时间：
2022
期刊：
Encyclopedia of Big Data
影响因子：
--
作者：
C. Strasser;Oran Viriyincy CC
通讯作者：
Oran Viriyincy CC
非线性演化方程参数估计技术的数值研究
DOI：
--
发表时间：
1998
期刊：
Kybernetika (Praha)
影响因子：
--
作者：
A. Ackleh;R. Ferdinand;S. Reich
通讯作者：
S. Reich