Robust forecasting using predictive generalized synchronization in reservoir computing

Platt, Jason A.; Wong, Adrian S.; Clark, Randall; Penny, Stephen G.

doi:10.1063/5.0066013

Cited by 20 publications

(20 citation statements)

References 73 publications

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“…The ability to set the macro-scale properties of the network and the quick training of the micro-scale parameter through linear regression couple together to allow the RC to be trained and deployed quickly and easily. Additionally, the RC has been shown not only to give good predictions but also to react like a physical model to perturbations in the system state (shown as the reproduction of the LEs) [28,31,54]. This property is crucial for applications in numerical weather prediction and other fields where it is important to produce both a forecast as well as an uncertainty estimate of that forecast.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…As described in detail by [28,54], the RC works by making use of the concept of generalized synchronization (GS) [56]. The definition of GS is: for a drive system u ∈ R D and response system r ∈ R N , they are synchronized if there exists a function ψ such that r = ψ(u) [56].…”

Section: Generalized Synchronizationmentioning

confidence: 99%

“…Intuitively this implies that the dynamics of the response system are entirely predictable from the history of the input; in RC, for a contracting system, this property is related to the "echo state property" [17] and "fading memory" [57]. The requirement to find a matrix W out such that W out r(t) = u(t) is tantamount to finding a linear approximation to the local inverse of the generalized synchronization function-we call this statement predictive generalized synchronization [54]. We would like to note that the statement of the existence of the inverse of ψ is in general not a global, but a local property due to the necessity of ψ being differentiable [58] for ψ −1 to exist.…”

Section: Generalized Synchronizationmentioning

confidence: 99%

“…As shown by Platt et.al., [54], the metric that best represents the ideal behavior of the RC-good short-term predictions coupled with "physical" (the forecast RC stays on the synchronization manifold M) long-term forecasts-is best represented by the reproduction of the input system's LEs. In practice the LEs can be difficult to calculate from highdimensional experimental data and computationally expensive for the RC.…”

Section: Forecast Testing Metricmentioning

confidence: 99%

“…( 7) RC match the LEs of the input data generated from the dynamical system f u then the RC is said to have "reconstructed" the attractor [28]. A reconstructed attractor is strongly correlated with properties such as the physicality and robustness of forecasts [54]. The LEs of f u can be estimated from the data with no knowledge of the dynamics [52].…”

Section: Application To Reservoir Computingmentioning

confidence: 99%

See 4 more Smart Citations

A Systematic Exploration of Reservoir Computing for Forecasting Complex Spatiotemporal Dynamics

Platt¹,

Penny²,

Smith³

et al. 2022

Preprint

Self Cite

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A reservoir computer (RC) is a type of simplified recurrent neural network architecture that has demonstrated success in the prediction of spatiotemporally chaotic dynamical systems. A further advantage of RC is that it reproduces intrinsic dynamical quantities essential for its incorporation into numerical forecasting routines such as the ensemble Kalman filter-used in numerical weather prediction to compensate for sparse and noisy data. We explore here the architecture and design choices for a "best in class" RC for a number of characteristic dynamical systems, and then show the application of these choices in scaling up to larger models using localization. Our analysis points to the importance of large scale parameter optimization. We also note in particular the importance of including input bias in the RC design, which has a significant impact on the forecast skill of the trained RC model. In our tests, the the use of a nonlinear readout operator does not affect the forecast time or the stability of the forecast. The effects of the reservoir dimension, spinup time, amount of training data, normalization, noise, and the RC time step are also investigated. While we are not aware of a generally accepted best reported mean forecast time for different models in the literature, we report over a factor of 2 increase in the mean forecast time compared to the best performing RC model of [1] for the 40 dimensional spatiotemporally chaotic Lorenz 1996 dynamics, and we are able to accomplish this using a smaller reservoir size.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Generalized Synchronizationmentioning

confidence: 99%

Section: Generalized Synchronizationmentioning

confidence: 99%

Section: Forecast Testing Metricmentioning

confidence: 99%

Section: Application To Reservoir Computingmentioning

confidence: 99%

See 3 more Smart Citations

A Systematic Exploration of Reservoir Computing for Forecasting Complex Spatiotemporal Dynamics

Platt¹,

Penny²,

Smith³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

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Experimental Demonstration of High‐Performance Physical Reservoir Computing with Nonlinear Interfered Spin Wave Multidetection

Namiki,

Nishioka,

Yamaguchi

et al. 2023

Advanced Intelligent Systems

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Physical reservoir computing, which is a promising method for the implementation of highly efficient artificial intelligence devices, requires a physical system with nonlinearity, fading memory, and the ability to map in high dimensions. Although it is expected that spin wave interference can perform as highly efficient reservoir computing in some micromagnetic simulations, there has been no experimental verification to date. Herein, reservoir computing is demonstrated that utilizes multidetected nonlinear spin wave interference in an yttrium‐iron‐garnet single crystal. The subject computing system achieves excellent performance when used for hand‐written digit recognition, second‐order nonlinear dynamical tasks, and nonlinear autoregressive moving average (NARMA). It is of particular note that normalized mean square errors for NARMA2 and second‐order nonlinear dynamical tasks are 1.81 × 10−2 and 8.37 × 10−5, respectively, which are the lowest figures for any experimental physical reservoir so far reported. Said high performance is achieved with higher nonlinearity and the large memory capacity of interfered spin wave multidetection.

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Generalized outer synchronization and parameters identification of uncertain delayed hypernetworks with stochastic noises

Wang

Lü

et al. 2023

Intl J Robust & Nonlinear

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Synchronization of hypernetworks has been extensively researched due to its potential applications in various contexts, such as secure communications and power grid engineering. However, the existing works thus far have primarily been devoted to inner synchronization or complete outer synchronization with identical node dynamics and topology structures. To investigate harmonious coexistence between two networks with nonidentical node dynamics and reduce control costs as well, this paper focuses on generalized outer synchronization (GOS) and parameters identification of uncertain delayed hypernetworks with stochastic noises. Regardless of whether the node parameters are known or not, based on Lyapunov stability and the LaSalle-type invariance principle for stochastic differential equations with multiple delays, some sufficient conditions are exhibited to reach GOS almost surely via adaptive control schemes.Moreover, the unknown node parameter vectors are identified by the designed updating laws. In addition, some corollaries are deduced and indicate that our proposed methods contain single-layer networks and complete synchronization methods as special cases. Furthermore, numerical simulations are provided to verify the effectiveness of our approaches. In particular, it is revealed that network parameters, including time delays, coupling strengths, and noise intensities, have an impact on the performance of the proposed algorithms.

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Robust forecasting using predictive generalized synchronization in reservoir computing

Cited by 20 publications

References 73 publications

A Systematic Exploration of Reservoir Computing for Forecasting Complex Spatiotemporal Dynamics

A Systematic Exploration of Reservoir Computing for Forecasting Complex Spatiotemporal Dynamics

Experimental Demonstration of High‐Performance Physical Reservoir Computing with Nonlinear Interfered Spin Wave Multidetection

Generalized outer synchronization and parameters identification of uncertain delayed hypernetworks with stochastic noises

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