Chaotic attractor reconstruction using small reservoirs -- the influence of topology
arXiv:2402.16888 · doi:10.1088/2632-2153/ad6ee8
Abstract
Forecasting timeseries based upon measured data is needed in a wide range of applications and has been the subject of extensive research. A particularly challenging task is the forecasting of timeseries generated by chaotic dynamics. In recent years reservoir computing has been shown to be an effective method of forecasting chaotic dynamics and reconstructing chaotic attractors from data. In this work strides are made toward smaller and lower complexity reservoirs with the goal of improved hardware implementability and more reliable production of adequate surrogate models. We show that a reservoir of uncoupled nodes more reliably produces long term timeseries predictions than complex reservoir topologies. We then link the improved attractor reconstruction of the uncoupled reservoir with smaller spectral radii of the resulting surrogate systems. These results indicate that, the node degree plays an important role in determining whether the desired dynamics will be stable in the autonomous surrogate system which is attained via closed-loop operation of the trained reservoir. In terms of hardware implementability, uncoupled nodes would allow for greater freedom in the hardware architecture because no complex coupling setups are needed and because, for uncoupled nodes, the system response is equivalent for space and time multiplexing.
References in corpus (17)
- Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
- Optoelectronic Reservoir Computing
- Using Machine Learning to Replicate Chaotic Attractors and Calculate Lyapunov Exponents from Data
- Next Generation Reservoir Computing
- Attractor Reconstruction by Machine Learning
- Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model
- Forecasting Chaotic Systems with Very Low Connectivity Reservoir Computers
- Embedding and Approximation Theorems for Echo State Networks
- Using a reservoir computer to learn chaotic attractors, with applications to chaos synchronisation and cryptography
- Temporal Information Processing on Noisy Quantum Computers
- Time Series Quantum Reservoir Computing with Weak and Projective Measurements
- Good and bad predictions: Assessing and improving the replication of chaotic attractors by means of reservoir computing
- Hybrid quantum-classical reservoir computing of thermal convection flow
- An array of microresonators as a Photonic Extreme Learning Machine
- Solving the time-complexity problem and tuning the performance of quantum reservoir computing by artificial memory restriction
- Time-Delayed Reservoir Computing Based on Dual-Waveband Quantum-Dot Spin-Polarized Vertical Cavity Surface-Emitting Laser
- Effect of temporal resolution on the reproduction of chaotic dynamics via reservoir computing