Designing chaotic attractors: A semisupervised approach

Physical review. E, Journal Year: 2025, Volume and Issue: 111(3)

Published: March 11, 2025

Chaotic dynamics are ubiquitous in nature and useful engineering, but their geometric design can be challenging. Here we propose a method using reservoir computing to generate chaos with desired shape by providing periodic orbit as template, called skeleton. We exploit bifurcation of the intentionally induce unsuccessful training skeleton, revealing inherent chaos. The emergence this untrained attractor, resulting from interaction between skeleton reservoir's intrinsic dynamics, offers semisupervised framework for designing

Language: Английский

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Data-driven ordinary-differential-equation modeling of high-frequency complex dynamics via a low-frequency dynamics model

Physical review. E, Journal Year: 2025, Volume and Issue: 111(1)

Published: Jan. 7, 2025

In our previous paper [N. Tsutsumi et al., Chaos 32, 091101 (2022)10.1063/5.0100166], we proposed a method for constructing system of differential equations chaotic behavior from only observable deterministic time series, which call the radial function-based regression (RfR) method. However, when targeted variable's is rather complex, direct application RfR does not function well. this study, propose modeling such dynamics, including high-frequency intermittent fluid flow, by considering another variable (base variable) showing relatively simple, less behavior. We construct an autonomous joint model composed two parts: first base variable, and other concerns being affected term involving to demonstrate complex dynamics. The constructed succeeded in inferring short trajectory but also reconstructing sets statistical properties obtained long as density distributions actual

Language: Английский

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Learning High-Dimensional Chaos Based on an Echo State Network with Homotopy Transformation

Mathematics, Journal Year: 2025, Volume and Issue: 13(6), P. 894 - 894

Published: March 7, 2025

Learning high-dimensional chaos is a complex and challenging problem because of its initial value-sensitive dependence. Based on an echo state network (ESN), we introduce homotopy transformation in topological theory to learn chaos. On the premise maintaining basic properties, our model can obtain key features for learning through continuous between different activation functions, achieving optimal balance nonlinearity linearity enhance generalization capability model. In experimental part, choose Lorenz system, Mackey–Glass (MG) Kuramoto–Sivashinsky (KS) system as examples, verify superiority by comparing it with other models. For some systems, prediction error be reduced two orders magnitude. The results show that addition improve modeling ability spatiotemporal chaotic this demonstrates potential application dynamic time series analysis.

Language: Английский

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Reservoir computing with the minimum description length principle

Chaos An Interdisciplinary Journal of Nonlinear Science, Journal Year: 2025, Volume and Issue: 35(4)

Published: April 1, 2025

We use the minimum description length (MDL) principle, which is an information-theoretic criterion for model selection, to determine echo-state network readout subsets. find that this method of MDL subset selection improves accuracy when forecasting Lorenz, Rössler, and Thomas attractors. It also performance benefit occurs higher-order terms are included in layer. provide explanation these improvements decreased linear dependence improved consistency.

Language: Английский

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Reconstruction of neuromorphic dynamics from a single scalar time series using variational autoencoder and neural network map

Chaos Solitons & Fractals, Journal Year: 2024, Volume and Issue: 191, P. 115818 - 115818

Published: Nov. 30, 2024

Language: Английский

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