论文标题
随机数据驱动的变异多尺度减少订单模型
Stochastic Data-Driven Variational Multiscale Reduced Order Models
论文作者
论文摘要
通过轨迹数据驱动的减少订单模型（ROM）倾向于对训练数据敏感，因此缺乏鲁棒性。我们建议从由随机初始条件的多个轨迹组成的数据中构造出强大的随机ROM闭合（S-ROM）。 S-ROM是一个低维时序列模型，用于从数据中推断出的主导正交分解（POD）模式的系数。因此，它实现了空间和时间的减少，从而导致模拟数量比完整模型快。我们表明，当轨迹数量增加时，S-ROM中的估计POD模式和参数会收敛。因此，当训练数据大小增加时，S-ROM很健壮。我们在具有粘度$ν= 0.002 $的1D汉堡方程式上演示了S-ROM，并且具有随机的初始条件。数值结果验证了收敛性。此外，S-ROM从新的初始条件和预测时间远远超出了训练范围，并量化了由于未解决的量表而导致的不确定性的传播，从而使轨迹的准确预测准确。
Trajectory-wise data-driven reduced order models (ROMs) tend to be sensitive to training data, and thus lack robustness. We propose to construct a robust stochastic ROM closure (S-ROM) from data consisting of multiple trajectories from random initial conditions. The S-ROM is a low-dimensional time series model for the coefficients of the dominating proper orthogonal decomposition (POD) modes inferred from data. Thus, it achieves reduction both space and time, leading to simulations orders of magnitude faster than the full order model. We show that both the estimated POD modes and parameters in the S-ROM converge when the number of trajectories increases. Thus, the S-ROM is robust when the training data size increases. We demonstrate the S-ROM on a 1D Burgers equation with a viscosity $ν= 0.002$ and with random initial conditions. The numerical results verify the convergence. Furthermore, the S-ROM makes accurate trajectory-wise predictions from new initial conditions and with a prediction time far beyond the training range, and it quantifies the spread of uncertainties due to the unresolved scales.
