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Article ; Online: Controlling chaotic maps using next-generation reservoir computing.

Kent, Robert M / Barbosa, Wendson A S / Gauthier, Daniel J

2024 Volume 34, Issue 2

Abstract: In this work, we combine nonlinear system control techniques with next-generation reservoir computing, a best-in-class machine learning approach for predicting the behavior of dynamical systems. We demonstrate the performance of the controller in a ... ...

Abstract	In this work, we combine nonlinear system control techniques with next-generation reservoir computing, a best-in-class machine learning approach for predicting the behavior of dynamical systems. We demonstrate the performance of the controller in a series of control tasks for the chaotic Hénon map, including controlling the system between unstable fixed points, stabilizing the system to higher order periodic orbits, and to an arbitrary desired state. We show that our controller succeeds in these tasks, requires only ten data points for training, can control the system to a desired trajectory in a single iteration, and is robust to noise and modeling error.
Language	English
Publishing date	2024-02-02
Publishing country	United States
Document type	Journal Article
ZDB-ID	1472677-4
ISSN	1089-7682 ; 1054-1500
ISSN (online)	1089-7682
ISSN	1054-1500
DOI	10.1063/5.0165864
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Controlling chaos using edge computing hardware.

Kent, Robert M / Barbosa, Wendson A S / Gauthier, Daniel J

Nature communications

2024 Volume 15, Issue 1, Page(s) 3886

Abstract: Machine learning provides a data-driven approach for creating a digital twin of a system - a digital model used to predict the system behavior. Having an accurate digital twin can drive many applications, such as controlling autonomous systems. Often, ... ...

Abstract	Machine learning provides a data-driven approach for creating a digital twin of a system - a digital model used to predict the system behavior. Having an accurate digital twin can drive many applications, such as controlling autonomous systems. Often, the size, weight, and power consumption of the digital twin or related controller must be minimized, ideally realized on embedded computing hardware that can operate without a cloud-computing connection. Here, we show that a nonlinear controller based on next-generation reservoir computing can tackle a difficult control problem: controlling a chaotic system to an arbitrary time-dependent state. The model is accurate, yet it is small enough to be evaluated on a field-programmable gate array typically found in embedded devices. Furthermore, the model only requires 25.0
Language	English
Publishing date	2024-05-08
Publishing country	England
Document type	Journal Article
ZDB-ID	2553671-0
ISSN	2041-1723 ; 2041-1723
ISSN (online)	2041-1723
ISSN	2041-1723
DOI	10.1038/s41467-024-48133-3
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Qubit-Based Clock Synchronization for QKD Systems Using a Bayesian Approach.

Cochran, Roderick D / Gauthier, Daniel J

Entropy (Basel, Switzerland)

2021 Volume 23, Issue 8

Abstract: Quantum key distribution (QKD) systems provide a method for two users to exchange a provably secure key. Synchronizing the users' clocks is an essential step before a secure key can be distilled. Qubit-based synchronization protocols directly use the ... ...

Abstract	Quantum key distribution (QKD) systems provide a method for two users to exchange a provably secure key. Synchronizing the users' clocks is an essential step before a secure key can be distilled. Qubit-based synchronization protocols directly use the transmitted quantum states to achieve synchronization and thus avoid the need for additional classical synchronization hardware. Previous qubit-based synchronization protocols sacrifice secure key either directly or indirectly, and all known qubit-based synchronization protocols do not efficiently use all publicly available information published by the users. Here, we introduce a Bayesian probabilistic algorithm that incorporates all published information to efficiently find the clock offset without sacrificing any secure key. Additionally, the output of the algorithm is a probability, which allows us to quantify our confidence in the synchronization. For demonstration purposes, we present a model system with accompanying simulations of an efficient three-state BB84 prepare-and-measure protocol with decoy states. We use our algorithm to exploit the correlations between Alice's published basis and mean photon number choices and Bob's measurement outcomes to probabilistically determine the most likely clock offset. We find that we can achieve a 95 percent synchronization confidence in only 4140 communication bin widths, meaning we can tolerate clock drift approaching 1 part in 4140 in this example when simulating this system with a dark count probability per communication bin width of 8×10-4 and a received mean photon number of 0.01.
Language	English
Publishing date	2021-07-30
Publishing country	Switzerland
Document type	Journal Article
ZDB-ID	2014734-X
ISSN	1099-4300 ; 1099-4300
ISSN (online)	1099-4300
ISSN	1099-4300
DOI	10.3390/e23080988
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: High-speed harvesting of random numbers.

Fischer, Ingo / Gauthier, Daniel J

Science (New York, N.Y.)

2021 Volume 371, Issue 6532, Page(s) 889–890

MeSH term(s)	Lasers ; Light
Language	English
Publishing date	2021-02-25
Publishing country	United States
Document type	Journal Article ; Comment
ZDB-ID	128410-1
ISSN	1095-9203 ; 0036-8075
ISSN (online)	1095-9203
ISSN	0036-8075
DOI	10.1126/science.abg5445
Database	MEDical Literature Analysis and Retrieval System OnLINE

In stock of ZB MED Cologne/Königswinter

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Zs.MG 77: Show issues

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Article ; Online: Learning unseen coexisting attractors.

Gauthier, Daniel J / Fischer, Ingo / Röhm, André

Chaos (Woodbury, N.Y.)

2022 Volume 32, Issue 11, Page(s) 113107

Abstract: Reservoir computing is a machine learning approach that can generate a surrogate model of a dynamical system. It can learn the underlying dynamical system using fewer trainable parameters and, hence, smaller training data sets than competing approaches. ... ...

Abstract	Reservoir computing is a machine learning approach that can generate a surrogate model of a dynamical system. It can learn the underlying dynamical system using fewer trainable parameters and, hence, smaller training data sets than competing approaches. Recently, a simpler formulation, known as next-generation reservoir computing, removed many algorithm metaparameters and identified a well-performing traditional reservoir computer, thus simplifying training even further. Here, we study a particularly challenging problem of learning a dynamical system that has both disparate time scales and multiple co-existing dynamical states (attractors). We compare the next-generation and traditional reservoir computer using metrics quantifying the geometry of the ground-truth and forecasted attractors. For the studied four-dimensional system, the next-generation reservoir computing approach uses ∼ 1.7 × less training data, requires
Language	English
Publishing date	2022-11-28
Publishing country	United States
Document type	Journal Article
ZDB-ID	1472677-4
ISSN	1089-7682 ; 1054-1500
ISSN (online)	1089-7682
ISSN	1054-1500
DOI	10.1063/5.0116784
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Book ; Online: Controlling Chaotic Maps using Next-Generation Reservoir Computing

Kent, Robert M. / Barbosa, Wendson A. S. / Gauthier, Daniel J.

2023

Abstract	In this work, we combine nonlinear system control techniques with next-generation reservoir computing, a best-in-class machine learning approach for predicting the behavior of dynamical systems. We demonstrate the performance of the controller in a series of control tasks for the chaotic H\'enon map, including controlling the system between unstable fixed-points, stabilizing the system to higher order periodic orbits, and to an arbitrary desired state. We show that our controller succeeds in these tasks, requires only 10 data points for training, can control the system to a desired trajectory in a single iteration, and is robust to noise and modeling error. Comment: 9 pages, 8 figures
Keywords	Computer Science - Machine Learning ; Computer Science - Neural and Evolutionary Computing ; Electrical Engineering and Systems Science - Systems and Control ; Nonlinear Sciences - Chaotic Dynamics
Publishing date	2023-07-07
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: Model-free inference of unseen attractors: Reconstructing phase space features from a single noisy trajectory using reservoir computing.

Röhm, André / Gauthier, Daniel J / Fischer, Ingo

Chaos (Woodbury, N.Y.)

2021 Volume 31, Issue 10, Page(s) 103127

Abstract: Reservoir computers are powerful tools for chaotic time series prediction. They can be trained to approximate phase space flows and can thus both predict future values to a high accuracy and reconstruct the general properties of a chaotic attractor ... ...

Abstract	Reservoir computers are powerful tools for chaotic time series prediction. They can be trained to approximate phase space flows and can thus both predict future values to a high accuracy and reconstruct the general properties of a chaotic attractor without requiring a model. In this work, we show that the ability to learn the dynamics of a complex system can be extended to systems with multiple co-existing attractors, here a four-dimensional extension of the well-known Lorenz chaotic system. We demonstrate that a reservoir computer can infer entirely unexplored parts of the phase space; a properly trained reservoir computer can predict the existence of attractors that were never approached during training and, therefore, are labeled as unseen. We provide examples where attractor inference is achieved after training solely on a single noisy trajectory.
Language	English
Publishing date	2021-10-31
Publishing country	United States
Document type	Journal Article
ZDB-ID	1472677-4
ISSN	1089-7682 ; 1054-1500
ISSN (online)	1089-7682
ISSN	1054-1500
DOI	10.1063/5.0065813
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Learning spatiotemporal chaos using next-generation reservoir computing.

Barbosa, Wendson A S / Gauthier, Daniel J

Chaos (Woodbury, N.Y.)

2021 Volume 32, Issue 9, Page(s) 93137

Abstract: Forecasting the behavior of high-dimensional dynamical systems using machine learning requires efficient methods to learn the underlying physical model. We demonstrate spatiotemporal chaos prediction using a machine learning architecture that, when ... ...

Abstract	Forecasting the behavior of high-dimensional dynamical systems using machine learning requires efficient methods to learn the underlying physical model. We demonstrate spatiotemporal chaos prediction using a machine learning architecture that, when combined with a next-generation reservoir computer, displays state-of-the-art performance with a computational time
Language	English
Publishing date	2021-10-04
Publishing country	United States
Document type	Journal Article
ZDB-ID	1472677-4
ISSN	1089-7682 ; 1054-1500
ISSN (online)	1089-7682
ISSN	1054-1500
DOI	10.1063/5.0098707
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Book ; Online: Learning unseen coexisting attractors

Gauthier, Daniel J. / Fischer, Ingo / Röhm, André

2022

Abstract: Reservoir computing is a machine learning approach that can generate a surrogate model of a dynamical system. It can learn the underlying dynamical system using fewer trainable parameters and hence smaller training data sets than competing approaches. ... ...

Abstract	Reservoir computing is a machine learning approach that can generate a surrogate model of a dynamical system. It can learn the underlying dynamical system using fewer trainable parameters and hence smaller training data sets than competing approaches. Recently, a simpler formulation, known as next-generation reservoir computing, removes many algorithm metaparameters and identifies a well-performing traditional reservoir computer, thus simplifying training even further. Here, we study a particularly challenging problem of learning a dynamical system that has both disparate time scales and multiple co-existing dynamical states (attractors). We compare the next-generation and traditional reservoir computer using metrics quantifying the geometry of the ground-truth and forecasted attractors. For the studied four-dimensional system, the next-generation reservoir computing approach uses $\sim 1.7 \times$ less training data, requires $10^3 \times$ shorter `warm up' time, has fewer metaparameters, and has an $\sim 100\times$ higher accuracy in predicting the co-existing attractor characteristics in comparison to a traditional reservoir computer. Furthermore, we demonstrate that it predicts the basin of attraction with high accuracy. This work lends further support to the superior learning ability of this new machine learning algorithm for dynamical systems. Comment: 8 pages, 7 figures
Keywords	Computer Science - Machine Learning ; Nonlinear Sciences - Chaotic Dynamics
Subject code	006
Publishing date	2022-07-28
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Book ; Online: Learning Spatiotemporal Chaos Using Next-Generation Reservoir Computing

Barbosa, Wendson A. S. / Gauthier, Daniel J.

2022

Abstract	Forecasting the behavior of high-dimensional dynamical systems using machine learning requires efficient methods to learn the underlying physical model. We demonstrate spatiotemporal chaos prediction using a machine learning architecture that, when combined with a next-generation reservoir computer, displays state-of-the-art performance with a computational time $10^3-10^4$ times faster for training process and training data set $\sim 10^2$ times smaller than other machine learning algorithms. We also take advantage of the translational symmetry of the model to further reduce the computational cost and training data, each by a factor of $\sim$10. Comment: 11 pages, 10 figures
Keywords	Computer Science - Machine Learning ; Computer Science - Neural and Evolutionary Computing ; Nonlinear Sciences - Chaotic Dynamics
Publishing date	2022-03-24
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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