论文标题
随机汉堡方程的数据驱动模型降低
Data-driven model reduction for stochastic Burgers equations
论文作者
论文摘要
我们为1D随机汉堡方程提供了一类有效的参数闭合模型。将其作为流图的统计学习，我们通过表示未解决的高波数傅立叶模式作为解决变量轨迹的功能来得出参数形式。还原的模型是非线性自动进度（NAR）时间序列模型，其系数从数据中估算为最小二乘。 NAR模型可以准确地重现能谱，不变密度和自相关。利用NAR模型的简单性，我们研究了最大和最佳的时空降低。空间维度的降低是无限的，具有两个傅立叶模式的NAR模型可以很好地表现。 NAR模型的稳定性限制了时间的缩短，其最大时间步长比K-Mode Galerkin系统小。我们报告了最佳时空减少的潜在标准：NAR模型在k-Mode Galerkin系统的平均CFL数量与完整模型一致的时间步骤中实现了能量谱的最小相对误差。
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 variables' 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 and optimal 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 CFL number agrees with the full model's.
