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Related Experiment Video

Updated: Jan 3, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

Learning the tangent space of dynamical instabilities from data.

Antoine Blanchard¹, Themistoklis P Sapsis¹

¹Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

Chaos (Woodbury, N.Y.)

|November 30, 2019

Summary

Neural networks map dynamical system states to optimally time-dependent (OTD) modes, identifying instability directions directly from data. This creates a phase space cartography for predicting and controlling instabilities.

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Area of Science:

Dynamical Systems Theory
Machine Learning
Nonlinear Dynamics

Background:

Optimally time-dependent (OTD) modes identify instability directions in dynamical systems.
These modes depend on the system's current state, not its history.
Directly learning this mapping from data is computationally challenging.

Purpose of the Study:

To develop a data-driven method for learning the pointwise mapping from phase space to OTD space.
To create a cartography of instability directions within the phase space.
To explore implications for predicting and controlling dynamical instabilities.

Main Methods:

Utilizing neural networks to learn the mapping from system state to OTD modes.
Training the network on trajectory data from dynamical systems.
Analyzing the learned mapping to identify regions of high instability.

Main Results:

Successfully trained neural networks to accurately predict OTD modes from system states.
Generated a phase space cartography highlighting directions of greatest instability.
Demonstrated the potential for data-driven prediction and control of instabilities.

Conclusions:

Neural networks provide a powerful tool for learning complex mappings in dynamical systems.
The data-driven approach offers a new way to understand and manage system instabilities.
This work has significant implications for fields relying on the analysis of complex dynamics.