论文标题
数据驱动的建模和通过光谱子曼群的非可连接动力学预测
Data-Driven Modeling and Prediction of Non-Linearizable Dynamics via Spectral Submanifolds
论文作者
论文摘要
我们开发了一种方法，以构建来自代表具有非线性（或不可线化的）动力学系统的数据集的低维预测模型，其双曲线线性部分受外部强迫的影响，并具有有限的许多频率。我们的数据驱动的，稀疏的非线性模型作为在低维度上减少动力学的扩展正常形式获得，吸引了动力学系统的光谱次符号（SSM）。我们说明了数据驱动的SSM在高维数值数据集以及涉及梁振荡，涡流脱落和斜孔的高维数值数据集上的功能。我们发现，对未强制性数据训练的SSM还原还可以预测在其他外部强迫下准确地预测非线性响应。
We develop a methodology to construct low-dimensional predictive models from data sets representing essentially nonlinear (or non-linearizable) dynamical systems with a hyperbolic linear part that are subject to external forcing with finitely many frequencies. Our data-driven, sparse, nonlinear models are obtained as extended normal forms of the reduced dynamics on low-dimensional, attracting spectral submanifolds (SSMs) of the dynamical system. We illustrate the power of data-driven SSM reduction on high-dimensional numerical data sets and experimental measurements involving beam oscillations, vortex shedding and sloshing in a water tank. We find that SSM reduction trained on unforced data also predicts nonlinear response accurately under additional external forcing.
