Model-free inference of unseen attractors: Reconstructing phase space features from a single noisy trajectory using...

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Machine Learning

Background:

• Reservoir computers excel at chaotic time series prediction by approximating phase space flows.
• They can reconstruct attractor properties without explicit system models.
• Extending this capability to systems with multiple co-existing attractors is a significant challenge.

Purpose of the Study:

• To investigate the capability of reservoir computers in learning dynamics of systems with multiple co-existing attractors.
• To demonstrate attractor inference for entirely unexplored regions of phase space.
• To show prediction of unseen attractors after training on limited, noisy data.

Main Methods:

• Utilized a four-dimensional extension of the Lorenz chaotic system.
• Trained a reservoir computer on a single noisy trajectory from the system.
• Evaluated the reservoir computer's ability to predict and infer system dynamics and attractors.

Main Results:

• The reservoir computer successfully learned the dynamics of the complex system.
• It demonstrated the ability to infer entirely unexplored parts of the phase space.
• The system predicted the existence of unseen attractors not encountered during training.

Conclusions:

• Reservoir computers can extend their learning capabilities to complex systems with multiple co-existing attractors.
• Attractor inference is achievable even when trained on minimal, noisy data.
• This highlights the potential of reservoir computing for understanding complex dynamical systems.