Machine learning with observers predicts complex spatiotemporal behavior

Abstract

Chimeras and branching are two archetypical complex phenomena that appear in many physical systems; because of their different intrinsic dynamics, they delineate opposite non-trivial limits in the complexity of wave motion and present severe challenges in predicting chaotic and singular behavior in extended physical systems. We report on the long-term forecasting capability of Long Short-Term Memory (LSTM) and reservoir computing (RC) recurrent neural networks, when they are applied to the spatiotemporal evolution of turbulent chimeras in simulated arrays of coupled superconducting quantum interference devices (SQUIDs) or lasers, and branching in the electronic flow of two-dimensional graphene with random potential. We propose a new method in which we assign one LSTM network to each system node except for "observer" nodes which provide continual "ground truth" measurements as input; we refer to this method as "Observer LSTM" (OLSTM). We demonstrate that even a small number of observers greatly improves the data-driven (model-free) long-term forecasting capability of the LSTM networks and provide the framework for a consistent comparison between the RC and LSTM methods. We find that RC requires smaller training datasets than OLSTMs, but the latter requires fewer observers. Both methods are benchmarked against Feed-Forward neural networks (FNNs), also trained to make predictions with observers (OFNNs).

References in corpus (30)

• Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation
• Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
• Spontaneous synchrony in power-grid networks
• Chimera States in Mechanical Oscillator Networks
• Using Machine Learning to Replicate Chaotic Attractors and Calculate Lyapunov Exponents from Data
• Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators
• Coherent Branched Flow in a Two-Dimensional Electron Gas
• When Nonlocal Coupling Between Oscillators Becomes Stronger: Patched Synchrony or Multi-Chimera States
• Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks
• Coexistence of synchrony and incoherence in oscillatory media under nonlinear global coupling
• Robustness of chimera states for coupled FitzHugh-Nagumo oscillators
• Data-assisted reduced-order modeling of extreme events in complex dynamical systems
• The Physics and Applications of Superconducting Metamaterials
• Laser Chimeras as a paradigm for multi-stable patterns in complex systems
• A classification scheme for chimera states
• Chimera-like states in modular neural networks
• Progress in Superconducting Metamaterials
• Controlling unstable chaos: Stabilizing chimera states by feedback
• Quantum signatures of Chimera states
• Controlling Chimeras
• A Tweezer for Chimeras in Small Networks
• rf SQUID metamaterials
• Chimeras in SQUID Metamaterials
• Robust chimera states in SQUID metamaterials with local interactions
• A one-dimensional tunable magnetic metamaterial
• Realization and modeling of rf superconducting quantum interference device metamaterials
• Rogue events in complex linear and nonlinear photonic media
• Chimera states and synchronization in magnetically driven SQUID metamaterials
• Multi-clustered chimeras in large semiconductor laser arrays with nonlocal interactions
• Emergence and dynamical properties of stochastic branching in the electronic flows of disordered Dirac solids

Cited by in corpus (11)

• Hamiltonian neural networks for solving equations of motion
• Photonic extreme learning machine by free-space optical propagation
• Physical Symmetries Embedded in Neural Networks
• Machine Learning Link Inference of Noisy Delay-coupled Networks with Opto-Electronic Experimental Tests
• Identification of Chimera using Machine Learning
• Classification and prediction of wave chaotic systems with machine learning techniques
• CGKN: A Deep Learning Framework for Modeling Complex Dynamical Systems and Efficient Data Assimilation
• Analysis of chaotic dynamical systems with autoencoders
• Unsupervised Reservoir Computing for Solving Ordinary Differential Equations
• Quantum targeted energy transfer through machine learning tools
• Hybrid Backpropagation Parallel Reservoir Networks