Learning the tangent space of dynamical instabilities from data

Abstract

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.

Document Details

Document Type
Pub Defense Publication
Publication Date
Nov 01, 2019
Source ID
10.1063/1.5120830

Entities

People

  • Antoine Blanchard
  • Themistoklis Sapsis

Organizations

  • Army Research Office
  • Massachusetts Institute of Technology

Tags

Readers

  • Calculus or Mathematical Analysis
  • Neural Network Machine Learning.
  • Structural Dynamics.

Technology Areas

  • AI & ML
  • AI & ML - Machine Learning Algorithms
  • AI & ML - Neural Networks
  • Space
  • Space - Hall-Effect Thruster