Transfer learning of chaotic systems

Abstract

Can a neural network trained by the time series of system A be used to predict the evolution of system B? This problem, knowing as transfer learning in a broad sense, is of great importance in machine learning and data mining, yet has not been addressed for chaotic systems. Here we investigate transfer learning of chaotic systems from the perspective of synchronization-based state inference, in which a reservoir computer trained by chaotic system A is used to infer the unmeasured variables of chaotic system B, while A is different from B in either parameter or dynamics. It is found that if systems A and B are different in parameter, the reservoir computer can be well synchronized to system B. However, if systems A and B are different in dynamics, the reservoir computer fails to synchronize with system B in general. Knowledge transfer along a chain of coupled reservoir computers is also studied, and it is found that, although the reservoir computers are trained by different systems, the unmeasured variables of the driving system can be successfully inferred by the remote reservoir computer. Finally, by an experiment of chaotic pendulum, we show that the knowledge learned from the modeling system can be used to predict the evolution of the experimental system.

20 pages, 8 figures

References in corpus (10)

• Recent Advances in Physical Reservoir Computing: A Review
• Using Machine Learning to Replicate Chaotic Attractors and Calculate Lyapunov Exponents from Data
• Attractor Reconstruction by Machine Learning
• Forecasting Chaotic Systems with Very Low Connectivity Reservoir Computers
• Network Structure Effects in Reservoir Computers
• Good and bad predictions: Assessing and improving the replication of chaotic attractors by means of reservoir computing
• Combining Machine Learning with Knowledge-Based Modeling for Scalable Forecasting and Subgrid-Scale Closure of Large, Complex, Spatiotemporal Systems
• Consistency in Echo-State Networks
• Detection of Generalized Synchronization using Echo State Networks
• Machine learning prediction of critical transition and system collapse

Cited by in corpus (3)

• Anticipating synchronization with machine learning
• Learning Hamiltonian dynamics by reservoir computer
• Criticality in Reservoir Computer of Coupled Phase Oscillators