scholarly journals On explaining the surprising success of reservoir computing forecaster of chaos? The universal machine learning dynamical system with contrast to VAR and DMD

2021 ◽  
Vol 31 (1) ◽  
pp. 013108
Author(s):  
Erik Bollt
Keyword(s):  
Machine Learning ◽  
Dynamical System ◽  
Reservoir Computing ◽  
Universal Machine

scholarly journals Data-driven predictions of a multiscale Lorenz 96 chaotic system using machine-learning methods: reservoir computing, artificial neural network, and long short-term memory network

2020 ◽  
Vol 27 (3) ◽  
pp. 373-389 ◽  
Author(s):  
Ashesh Chattopadhyay ◽  
Pedram Hassanzadeh ◽  
Devika Subramanian
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Short Term Memory ◽  
Data Driven ◽  
Reservoir Computing ◽  
Short Term ◽  
Term Memory ◽  
Machine Learning Methods ◽  
Long Short Term Memory ◽  
Lorenz 96

Abstract. In this paper, the performance of three machine-learning methods for predicting short-term evolution and for reproducing the long-term statistics of a multiscale spatiotemporal Lorenz 96 system is examined. The methods are an echo state network (ESN, which is a type of reservoir computing; hereafter RC–ESN), a deep feed-forward artificial neural network (ANN), and a recurrent neural network (RNN) with long short-term memory (LSTM; hereafter RNN–LSTM). This Lorenz 96 system has three tiers of nonlinearly interacting variables representing slow/large-scale (X), intermediate (Y), and fast/small-scale (Z) processes. For training or testing, only X is available; Y and Z are never known or used. We show that RC–ESN substantially outperforms ANN and RNN–LSTM for short-term predictions, e.g., accurately forecasting the chaotic trajectories for hundreds of numerical solver's time steps equivalent to several Lyapunov timescales. The RNN–LSTM outperforms ANN, and both methods show some prediction skills too. Furthermore, even after losing the trajectory, data predicted by RC–ESN and RNN–LSTM have probability density functions (pdf's) that closely match the true pdf – even at the tails. The pdf of the data predicted using ANN, however, deviates from the true pdf. Implications, caveats, and applications to data-driven and data-assisted surrogate modeling of complex nonlinear dynamical systems, such as weather and climate, are discussed.

scholarly journals A substrate-independent framework to characterize reservoir computers

2019 ◽  
Vol 475 (2226) ◽  
pp. 20180723 ◽  
Author(s):  
Matthew Dale ◽  
Julian F. Miller ◽  
Susan Stepney ◽  
Martin A. Trefzer
Keyword(s):  
Dynamical System ◽  
Task Performance ◽  
Fading Memory ◽  
Reservoir Computing ◽  
Virtual Topology ◽  
Nonlinear Input ◽  
Definition Of ◽  
Substrate Independent ◽  
And Task

The reservoir computing (RC) framework states that any nonlinear, input-driven dynamical system (the reservoir ) exhibiting properties such as a fading memory and input separability can be trained to perform computational tasks. This broad inclusion of systems has led to many new physical substrates for RC. Properties essential for reservoirs to compute are tuned through reconfiguration of the substrate, such as change in virtual topology or physical morphology. As a result, each substrate possesses a unique ‘quality’—obtained through reconfiguration—to realize different reservoirs for different tasks. Here we describe an experimental framework to characterize the quality of potentially any substrate for RC. Our framework reveals that a definition of quality is not only useful to compare substrates, but can help map the non-trivial relationship between properties and task performance. In the wider context, the framework offers a greater understanding as to what makes a dynamical system compute, helping improve the design of future substrates for RC.

scholarly journals Graph Networks as a Universal Machine Learning Framework for Molecules and Crystals

2019 ◽  
Vol 31 (9) ◽  
pp. 3564-3572 ◽  
Author(s):  
Chi Chen ◽  
Weike Ye ◽  
Yunxing Zuo ◽  
Chen Zheng ◽  
Shyue Ping Ong
Keyword(s):  
Machine Learning ◽  
Learning Framework ◽  
Universal Machine

A Universal Machine Learning Algorithm for Large-Scale Screening of Materials

2020 ◽  
Vol 142 (8) ◽  
pp. 3814-3822 ◽  
Author(s):  
George S. Fanourgakis ◽  
Konstantinos Gkagkas ◽  
Emmanuel Tylianakis ◽  
George E. Froudakis
Keyword(s):  
Machine Learning ◽  
Large Scale ◽  
Learning Algorithm ◽  
Machine Learning Algorithm ◽  
Universal Machine ◽  
Large Scale Screening

scholarly journals Neuromorphic Computation With a Single Magnetic Domain Wall

2021 ◽  
Author(s):  
Razvan V. Ababei ◽  
Matthew O. A. Ellis ◽  
Ian T. Vidamour ◽  
Dhilan S. Devadasan ◽  
Dan A. Allwood ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Machine Learning ◽  
Domain Wall ◽  
Domain Walls ◽  
Magnetic Domain ◽  
Machine Learning Algorithms ◽  
Machine Learning Techniques ◽  
Complex Data ◽  
Reservoir Computing ◽  
Model Complex

Abstract Machine learning techniques are commonly used to model complex relationships but implementations on digital hardware are relatively inefficient due to poor matching between conventional computer architectures and the structures of the algorithms they are required to simulate. Neuromorphic devices, and in particular reservoir computing architectures, utilize the inherent properties of physical systems to implement machine learning algorithms and so have the potential to be much more efficient. In this work, we demonstrate that the dynamics of individual domain walls in magnetic nanowires are suitable for implementing the reservoir computing paradigm in hardware. We modelled the dynamics of a domain wall placed between two anti-notches in a nickel nanowire using both a 1d collective coordinates model and micromagnetic simulations. When driven by an oscillating magnetic field, the domain exhibits non-linear dynamics within the potential well created by the anti-notches that are analogous to those of the Duffing oscillator. We exploit the domain wall dynamics for reservoir computing by modulating the amplitude of the applied magnetic field to inject time-multiplexed input signals into the reservoir, and show how this allows us to perform machine learning tasks including: the classification of (1) sine and square waves; (2) spoken digits and (3) non-temporal 2D toy data and hand written digits. Our work lays the foundation for the creation of nanoscale neuromorphic devices in which individual magnetic domain walls are used to perform complex data analysis tasks.

scholarly journals A Novel, Potentially Universal Machine Learning Algorithm to Predict Complications in Total Knee Arthroplasty

2021 ◽  
Vol 10 ◽  
pp. 135-143
Author(s):  
Sai K. Devana ◽  
Akash A. Shah ◽  
Changhee Lee ◽  
Andrew R. Roney ◽  
Mihaela van der Schaar ◽  
...  
Keyword(s):  
Machine Learning ◽  
Total Knee Arthroplasty ◽  
Knee Arthroplasty ◽  
Learning Algorithm ◽  
Machine Learning Algorithm ◽  
Universal Machine ◽  
Total Knee

scholarly journals Neuromorphic computation with a single magnetic domain wall

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Razvan V. Ababei ◽  
Matthew O. A. Ellis ◽  
Ian T. Vidamour ◽  
Dhilan S. Devadasan ◽  
Dan A. Allwood ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Machine Learning ◽  
Domain Wall ◽  
Domain Walls ◽  
Magnetic Domain ◽  
Machine Learning Algorithms ◽  
Machine Learning Techniques ◽  
Complex Data ◽  
Reservoir Computing ◽  
Model Complex

AbstractMachine learning techniques are commonly used to model complex relationships but implementations on digital hardware are relatively inefficient due to poor matching between conventional computer architectures and the structures of the algorithms they are required to simulate. Neuromorphic devices, and in particular reservoir computing architectures, utilize the inherent properties of physical systems to implement machine learning algorithms and so have the potential to be much more efficient. In this work, we demonstrate that the dynamics of individual domain walls in magnetic nanowires are suitable for implementing the reservoir computing paradigm in hardware. We modelled the dynamics of a domain wall placed between two anti-notches in a nickel nanowire using both a 1D collective coordinates model and micromagnetic simulations. When driven by an oscillating magnetic field, the domain exhibits non-linear dynamics within the potential well created by the anti-notches that are analogous to those of the Duffing oscillator. We exploit the domain wall dynamics for reservoir computing by modulating the amplitude of the applied magnetic field to inject time-multiplexed input signals into the reservoir, and show how this allows us to perform machine learning tasks including: the classification of (1) sine and square waves; (2) spoken digits; and (3) non-temporal 2D toy data and hand written digits. Our work lays the foundation for the creation of nanoscale neuromorphic devices in which individual magnetic domain walls are used to perform complex data analysis tasks.

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