Robust and optimal sparse regression for nonlinear PDE models
Robust and optimal sparse regression for nonlinear PDE models
复制标题
DOI：
10.1063/1.5120861
复制
发表时间：
2019-10-01
期刊：
影响因子：
2.9
通讯作者：
Grigoriev, Roman O.
中科院分区：
文献类型：
--
作者：
Gurevich, Daniel R.;Reinbold, Patrick A. K.;Grigoriev, Roman O.
本文研究了如何利用稀疏回归和弱公式相结合的方法从噪声数据中直接识别非线性偏微分方程形式的时空动力学模型。使用四阶Kuramoto-Sivashinsky方程进行说明，我们展示了这种方法如何在低噪声和高噪声的限制下进行优化，实现比现有技术更好的数量级的精度。特别是，我们推导出模型的准确性，弱配方的参数，和数据的属性，如其空间和时间分辨率和噪声水平之间的比例关系。由AIP Publishing授权出版。
This paper investigates how models of spatiotemporal dynamics in the form of nonlinear partial differential equations can be identified directly from noisy data using a combination of sparse regression and weak formulation. Using the 4th-order Kuramoto-Sivashinsky equation for illustration, we show how this approach can be optimized in the limits of low and high noise, achieving accuracy that is orders of magnitude better than what existing techniques allow. In particular, we derive the scaling relation between the accuracy of the model, the parameters of the weak formulation, and the properties of the data, such as its spatial and temporal resolution and the level of noise. Published under license by AIP Publishing.