Learning the Tangent Space of Dynamical Instabilities from Data
This work addresses data-driven prediction and control of dynamical instabilities, which is incremental as it applies neural networks to an existing OTD framework.
The paper tackled the problem of identifying directions of strongest instabilities in dynamical systems by learning a mapping from phase space to optimally time-dependent (OTD) modes using neural networks, resulting in a cartography of these instabilities directly from data.
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, and not on the history of the trajectory. We leverage the power of neural networks to learn this "pointwise" mapping from phase space to OTD space directly from data. The result of the learning process is a cartography of directions associated with strongest instabilities in phase space. Implications for data-driven prediction and control of dynamical instabilities are discussed.