Attractor Reconstruction by Machine Learning

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.

References in corpus (4)

• Using Machine Learning to Replicate Chaotic Attractors and Calculate Lyapunov Exponents from Data
• Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks
• Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model
• Reservoir computing with a single time-delay autonomous Boolean node

Cited by in corpus (104)

• Next Generation Reservoir Computing
• Physical reservoir computing -- An introductory perspective
• Will Artificial Intelligence supersede Earth System and Climate Models?
• Deep learning of dynamics and signal-noise decomposition with time-stepping constraints
• On Explaining the Surprising Success of Reservoir Computing Forecaster of Chaos? The Universal Machine Learning Dynamical System with Contrasts to VAR and DMD
• Data-driven prediction of a multi-scale Lorenz 96 chaotic system using deep learning methods: Reservoir computing, ANN, and RNN-LSTM
• Boosting computational power through spatial multiplexing in quantum reservoir computing
• Zermelo's problem: Optimal point-to-point navigation in 2D turbulent flows using Reinforcement Learning
• Using reservoir computers to distinguish chaotic signals
• Learning dynamical systems from data: a simple cross-validation perspective
• Network Structure Effects in Reservoir Computers
• Machine-learning inference of fluid variables from data using reservoir computing
• Good and bad predictions: Assessing and improving the replication of chaotic attractors by means of reservoir computing
• Anticipating synchronization with machine learning
• Rapid Time Series Prediction with a Hardware-Based Reservoir Computer
• Do Reservoir Computers Work Best at the Edge of Chaos?
• Coupled nonlinear delay systems as deep convolutional neural networks
• Integrating Recurrent Neural Networks with Data Assimilation for Scalable Data-Driven State Estimation
• Reservoir computing with dipole-coupled nanomagnets
• Chaos on compact manifolds: Differentiable synchronizations beyond the Takens theorem
• Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systems
• Breaking Symmetries of the Reservoir Equations in Echo State Networks
• Optimizing Memory in Reservoir Computers
• Using reservoir computer to predict and prevent extreme events
• Multifunctionality in a Reservoir Computer
• Adaptable Hamiltonian neural networks
• Deep reconstruction of strange attractors from time series
• Data-driven Reconstruction of Nonlinear Dynamics from Sparse Observation
• Accuracy of neural networks for the simulation of chaotic dynamics: precision of training data vs precision of the algorithm
• Learning strange attractors with reservoir systems
• Catch-22s of reservoir computing
• Predicting Critical Transitions in Multiscale Dynamical Systems Using Reservoir Computing
• Finding nonlinear system equations and complex network structures from data: a sparse optimization approach
• Learn to Synchronize, Synchronize to Learn
• Inferring the dynamics of oscillatory systems using recurrent neural networks
• Dimension of Reservoir Computers
• Stability analysis of chaotic systems from data
• Reducing network size and improving prediction stability of reservoir computing
• The Echo Index and multistability in input-driven recurrent neural networks
• Dynamical system analysis of a data-driven model constructed by reservoir computing
• Time Shifts to Reduce the Size of Reservoir Computers
• Inferring Global Dynamics Using a Learning Machine
• Inferring Global Dynamics of a Black-Box System Using Machine Learning
• Copy the dynamics using a learning machine
• Machine Learning Link Inference of Noisy Delay-coupled Networks with Opto-Electronic Experimental Tests
• Hybridizing Traditional and Next-Generation Reservoir Computing to Accurately and Efficiently Forecast Dynamical Systems
• Risk bounds for reservoir computing
• Criticality in Reservoir Computer of Coupled Phase Oscillators
• Chaotic attractor reconstruction using small reservoirs -- the influence of topology
• Transfer learning of chaotic systems
• Identification of Chimera using Machine Learning
• Learning Continuous Chaotic Attractors with a Reservoir Computer
• Effective models and predictability of chaotic multiscale systems via machine learning
• Symmetry-Aware Reservoir Computing
• Stability Analysis of Reservoir Computers Dynamics via Lyapunov Functions
• Predicting multi-parametric dynamics of externally forced oscillator using reservoir computing and minimal data
• Reservoir Computers with Random and Optimized Time-Shifts
• Effect of temporal resolution on the reproduction of chaotic dynamics via reservoir computing
• Testing Dynamical System Variables for Reconstruction
• Learning unidirectional coupling using echo-state network
• Machine-learning construction of a model for a macroscopic fluid variable using the delay-coordinate of a scalar observable
• Reduced-order adaptive synchronization in a chaotic neural network with parameter mismatch: A dynamical system vs. machine learning approach
• Dynamical analysis of a parameter-aware reservoir computer
• Role of assortativity in predicting burst synchronization using echo state network
• Sparse Symplectically Integrated Neural Networks
• On the Universal Transformation of Data-Driven Models to Control Systems
• Predicting high-dimensional heterogeneous time series employing generalized local states
• Supervised Chaotic Source Separation by a Tank of Water
• Initializing LSTM internal states via manifold learning
• Backpropagation on Dynamical Networks
• Estimating the master stability function from the time series of one oscillator via reservoir computing
• How more data can hurt: Instability and regularization in next-generation reservoir computing
• A Unifying Framework for Information Processing in Stochastically Driven Dynamical Systems
• Characterization of Fractal Basins Using Deep Convolutional Neural Networks
• Learning stochastic dynamical systems with neural networks mimicking the Euler-Maruyama scheme
• Learning Dynamics from Noisy Measurements using Deep Learning with a Runge-Kutta Constraint
• Deep Learning-based Analysis of Basins of Attraction
• Thermodynamic limit in learning period three
• Hierarchical deep learning-based adaptive time-stepping scheme for multiscale simulations
• Differentiable reservoir computing
• Computing with vortices: Bridging fluid dynamics and its information-processing capability
• Long-term prediction of El Niño-Southern Oscillation using reservoir computing with data-driven realtime filter
• Tailored minimal reservoir computing: on the bidirectional connection between nonlinearities in the reservoir and in data
• Input-dependence in quantum reservoir computing
• Learning Beyond Experience: Generalizing to Unseen State Space with Reservoir Computing
• Predicting three-dimensional chaotic systems with four qubit quantum systems
• The Recurrent Processing Unit: Hardware for High Speed Machine Learning
• Forecasting Using Reservoir Computing: The Role of Generalized Synchronization
• Improving the prediction of spatio-temporal chaos by combining parallel reservoir computing with dimensionality reduction
• Attractor-merging Crises and Intermittency in Reservoir Computing
• State-space systems as dynamic generative models
• Analysis on reservoir activation with the nonlinearity harnessed from solution-processed molybdenum disulfide
• Echoes of the Past: A Unified Perspective on Fading memory and Echo States
• Next-Generation Reservoir Computing for Dynamical Inference
• Long-term prediction of chaotic systems with recurrent neural networks
• Model-free inference of unseen attractors: Reconstructing phase space features from a single noisy trajectory using reservoir computing
• Incorporating Coupling Knowledge into Echo State Networks for Learning Spatiotemporally Chaotic Dynamics
• Universal set of Observables for Forecasting Physical Systems through Causal Embedding
• Invertible generalized synchronization: A putative mechanism for implicit learning in biological and artificial neural systems
• Stability of exoplanetary systems retrieved from scalar time series
• Advanced Techniques in Stability Analysis of Trans-Neptunian Objects
• Deep Chaos Synchronization
• Dynamics of reservoir computing for crises prediction
• Finite-time Lyaponov analysis of a trained reservoir computer