论文标题
非线性动力学系统的快速数据驱动模型降低
Fast data-driven model reduction for nonlinear dynamical systems
论文作者
论文摘要
我们提出了一种快速的方法，用于非线性数据驱动的模型将动态系统降低到其最慢的非谐波频谱亚亮体（SSM）上。我们使用观察到的数据来定位低维，吸引慢速SSM并计算出最大稀疏的近似值，以减少其上的动力学。最近发布的SSMLEARN算法使用隐式优化来拟合光谱亚策略，并将动力学减少到正常形式。在这里，我们提出了两种简化的算法，这些算法在某些假设下重新将流形拟合和正常形式计算为明确的问题。我们在数值和实验数据集上都表明，这些算法为基本非线性（或不可接线）动力学产生准确且稀疏的严格模型。新算法已大大简化，并提供了几个数量级的加速。
We present a fast method for nonlinear data-driven model reduction of dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs). We use observed data to locate a low-dimensional, attracting slow SSM and compute a maximally sparse approximation to the reduced dynamics on it. The recently released SSMLearn algorithm uses implicit optimization to fit a spectral submanifold to data and reduce the dynamics to the normal form. Here, we present two simplified algorithms, which reformulate manifold fitting and normal form computation as explicit problems under certain assumptions. We show on both numerical and experimental datasets that these algorithms yield accurate and sparse rigorous models for essentially nonlinear (or non-linearizable) dynamics. The new algorithms are significantly simplified and provide a speedup of several orders of magnitude.
