Learning Spatiotemporal Chaos Using Next-Generation Reservoir Computing

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

doi:10.48550/arxiv.2203.13294

Cited by 2 publications

(4 citation statements)

References 22 publications

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“…We do not enforce this symmetry in the NG-RC feature vector, but we see that the NG-RC model properly learns the symmetry. 13,17 Beyond 330 time units, the trajectories diverge because of the chaotic nature of the attractors, but the dynamics appears qualitatively to be part of the same attractor, which is verified by the error metrics given in Table III. Here, the error in the uvariable is somewhat larger than for the other chaotic attractor but is still only ∼ 1%.…”

Section: B Testing On the Torussupporting

confidence: 55%

“…Studies on spatio-temporal systems are already underway. 13 Also, we will explore using adapted basis functions or functions that focus on a region of phase space to interpolate between discontinuous regions.…”

Section: Discussionmentioning

confidence: 99%

“…This speed up is important for control applications and may find application in speeding up simulations of systems displaying spatio-temporal chaos. 13 Briefly, the NG-RC expresses the flow as…”

Section: Next-generation Reservoir Computingmentioning

confidence: 99%

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Learning unseen coexisting attractors

Gauthier¹,

Fischer²,

Röhm³

2022

Preprint

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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 ∼ 1.7× less training data, requires 10 3 × shorter 'warm up' time, has fewer metaparameters, and has an ∼ 100× higher accuracy in predicting the coexisting 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.Reservoir computing is a machine learning approach that is well suited to learning dynamical systems using a short sample of time-series data. It learns the underlying dynamical system so that the trained model serves as a surrogate or a 'digital twin' of the system, and it can reproduce behaviors not contained in the training data set. For chaotic systems, it can reproduce the associated strange attractor and other characteristics. Surprisingly, the reservoir computer can learn attractors of a dynamical that is has not seen when it is trained on time-series data from a single attractor that it has seen. Here, we show that a variant machine learning algorithm, known as a next-generation reservoir computer, can reproduce co-existing attractors and the associated basin of attractor using smaller training data sets and with higher accuracy than a traditional reservoir computer.

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Section: B Testing On the Torussupporting

confidence: 55%

Section: Discussionmentioning

confidence: 99%

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Learning unseen coexisting attractors

Gauthier¹,

Fischer²,

Röhm³

2022

Preprint

Self Cite

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show abstract

“…Finally, we note that Gauthier et al (2021) proposed a further simplification to the RC architecture based on insights from Bollt (2021) that unifies versions of RC with nonlinear vector autoregression (NVAR). For a variety of chaotic systems, this architecture has shown excellent prediction skill even with low order, polynomial-based feature vectors (Barbosa & Gauthier, 2022;Gauthier et al, 2021), despite requiring a much smaller hidden state and less training data. Considering all of these advancements, we are motivated to use these simple yet powerful single layer NVAR and ESN architectures to emulate turbulent geophysical fluid dynamics, and study how they are affected by temporal subsampling (see Section 3 for architecture details).…”

mentioning

confidence: 99%

Temporal Subsampling Diminishes Small Spatial Scales in Recurrent Neural Network Emulators of Geophysical Turbulence

Smith,

Penny,

Platt

et al. 2023

J Adv Model Earth Syst

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The immense computational cost of traditional numerical weather and climate models has sparked the development of machine learning (ML) based emulators. Because ML methods benefit from long records of training data, it is common to use data sets that are temporally subsampled relative to the time steps required for the numerical integration of differential equations. Here, we investigate how this often overlooked processing step affects the quality of an emulator's predictions. We implement two ML architectures from a class of methods called reservoir computing: (a) a form of Nonlinear Vector Autoregression (NVAR), and (b) an Echo State Network (ESN). Despite their simplicity, it is well documented that these architectures excel at predicting low dimensional chaotic dynamics. We are therefore motivated to test these architectures in an idealized setting of predicting high dimensional geophysical turbulence as represented by Surface Quasi‐Geostrophic dynamics. In all cases, subsampling the training data consistently leads to an increased bias at small spatial scales that resembles numerical diffusion. Interestingly, the NVAR architecture becomes unstable when the temporal resolution is increased, indicating that the polynomial based interactions are insufficient at capturing the detailed nonlinearities of the turbulent flow. The ESN architecture is found to be more robust, suggesting a benefit to the more expensive but more general structure. Spectral errors are reduced by including a penalty on the kinetic energy density spectrum during training, although the subsampling related errors persist. Future work is warranted to understand how the temporal resolution of training data affects other ML architectures.

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Learning Spatiotemporal Chaos Using Next-Generation Reservoir Computing

Cited by 2 publications

References 22 publications

Learning unseen coexisting attractors

Learning unseen coexisting attractors

Temporal Subsampling Diminishes Small Spatial Scales in Recurrent Neural Network Emulators of Geophysical Turbulence

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