Attractor Reconstruction by Machine Learning

2018/05/31 by Zhixin Lu, Brian R. Hunt, Edward Ott · 12 citations
Physics and Astronomy · #nlin.CD

paper · pdf · doi:10.1063/1.5039508

arxiv created 2018/06/18 · arxiv updated 2018/08/01

Abstract

A machine-learning approach called "reservoir computing" has been used successfully for short-term prediction and attractor reconstruction of chaotic dynamical systems from time series data. We present a theoretical framework that describes conditions under which reservoir computing can create an empirical model capable of skillful short-term forecasts and accurate long-term ergodic behavior. We illustrate this theory through numerical experiments. We also argue that the theory applies to certain other machine learning methods for time series prediction.

Cited by

• One-shot prediction of noise-induced bifurcations with reservoir computing
• Attractor reconstruction in attracting subspaces: Slow-spectrum preshaping for reservoir computing under partial observation
• Chaotic Oscillator Networks for Classification Tasks
• Adaptive Reservoir Computing for Multi-Scenario Chaotic System Forecasting
• Optimizing Reservoir Computing for Reconstructing Ergodic Properties
• Inferring bifurcation diagrams of two distinct chaotic systems by a single machine
• Finite-time Lyaponov analysis of a trained reservoir computer
• Stabilizing chaotic dynamical system reproduction in reservoir computing
• Data-driven characterization of spatiotemporal chaos using ensemble reservoir computing
• Tailored minimal reservoir computing: on the bidirectional connection between nonlinearities in the reservoir and in data
• Attractor-merging Crises and Intermittency in Reservoir Computing
• Revisiting multifunctionality in reservoir computing

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