Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Chaos. 2019 Nov;29(11):113120. doi: 10.1063/1.5120830.
For a large class of dynamical systems, the optimally time-dependent (OTD) modes, a set of deformable orthonormal tangent vectors that track directions of instabilities along any trajectory, are known to depend "pointwise" on the state of the system on the attractor but not on the history of the trajectory. We leverage the power of neural networks to learn this "pointwise" mapping from the phase space to OTD space directly from data. The result of the learning process is a cartography of directions associated with strongest instabilities in the phase space. Implications for data-driven prediction and control of dynamical instabilities are discussed.
对于一大类动力系统，最优时变（OTD）模式是一组可变形的正交切向量，它们沿着吸引子上的任何轨迹跟踪不稳定性的方向，已知其“逐点”取决于系统在吸引子上的状态，而不取决于轨迹的历史。我们利用神经网络的强大功能，直接从数据中学习从相空间到 OTD 空间的这种“逐点”映射。学习过程的结果是一张与相空间中最强不稳定性相关的方向图。讨论了其对动力不稳定性的数据驱动预测和控制的影响。
