Data-Driven Model Reduction for Stochastic Burgers Equations.
Data-Driven Model Reduction for Stochastic Burgers Equations.
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DOI：
10.3390/e22121360
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发表时间：
2020-11-30
期刊：
影响因子：
--
通讯作者：
Lu F
中科院分区：
文献类型：
--
作者：
Lu F
给出了一维随机Burgers方程的有效参数闭包模型。将其作为流程图的统计学习，我们通过将未解析的高波数傅里叶模式表示为已解析变量轨迹的泛函数来推导参数形式。简化后的模型是非线性自回归（NAR）时间序列模型，其系数由最小二乘法估计。NAR模型可以准确地再现能量谱、不变密度和自相关性。利用NAR模型的简单性，我们研究了最大时空约简。空间维数的降维是无限的，具有两种傅里叶模式的NAR模型表现良好。NAR模型的稳定性限制了时间的缩短，其最大时间步长小于k型Galerkin系统。我们报告了一个最优时空缩减的潜在准则：NAR模型在时间步长的能谱中实现了最小的相对误差，其中k模伽辽金系统的平均Courant-Friedrichs-Lewy （CFL）数与完整模型的CFL数一致。
We present a class of efficient parametric closure models for 1D stochastic Burgers equations. Casting it as statistical learning of the flow map, we derive the parametric form by representing the unresolved high wavenumber Fourier modes as functionals of the resolved variable’s trajectory. The reduced models are nonlinear autoregression (NAR) time series models, with coefficients estimated from data by least squares. The NAR models can accurately reproduce the energy spectrum, the invariant densities, and the autocorrelations. Taking advantage of the simplicity of the NAR models, we investigate maximal space-time reduction. Reduction in space dimension is unlimited, and NAR models with two Fourier modes can perform well. The NAR model’s stability limits time reduction, with a maximal time step smaller than that of the K-mode Galerkin system. We report a potential criterion for optimal space-time reduction: the NAR models achieve minimal relative error in the energy spectrum at the time step, where the K-mode Galerkin system’s mean Courant–Friedrichs–Lewy (CFL) number agrees with that of the full model.
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影响因子：
3.1
作者：
Choi, Youngsoo;Carlberg, Kevin
通讯作者：
Carlberg, Kevin
DOI：
10.1073/pnas.0500335102
发表时间：
2005-03-15
影响因子：
11.1
作者：
Chorin, AJ;Hald, OH
通讯作者：
Hald, OH
影响因子：
4.4
作者：
Li, Zhen;Bian, Xin;Karniadakis, George Em
通讯作者：
Karniadakis, George Em
DOI：
10.1073/pnas.1512080112
发表时间：
2015-08-11
影响因子：
11.1
作者：
Chorin, Alexandre J.;Lu, Fei
通讯作者：
Lu, Fei
影响因子：
3.4
作者：
Dolaptchiev, S. I.;Achatz, U.;Timofeyev, I.
通讯作者：
Timofeyev, I.