Colored linear inverse model: A data-driven method for studying dynamical systems with temporally correlated stochasticity
In real-world problems, environmental noise is often idealized as Gaussian white noise, despite potential temporal dependencies. The linear inverse model (LIM) is a class of data-driven methods that extract dynamic and stochastic information from finite time-series data of complex systems. In this s...
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-04-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.023042 |
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| author | Justin Lien Yan-Ning Kuo Hiroyasu Ando Shoichiro Kido |
| author_facet | Justin Lien Yan-Ning Kuo Hiroyasu Ando Shoichiro Kido |
| author_sort | Justin Lien |
| collection | DOAJ |
| description | In real-world problems, environmental noise is often idealized as Gaussian white noise, despite potential temporal dependencies. The linear inverse model (LIM) is a class of data-driven methods that extract dynamic and stochastic information from finite time-series data of complex systems. In this study, we introduce a new variant of LIM, called colored LIM, which models stochasticity using Ornstein-Uhlenbeck colored noise. Despite the nontrivial correlation between observable and colored noise, we show that colored LIM unveils the desired information merely from the correlation function of the observable. Therefore, this approach not only accounts for the memory effects of environmental noise, traditionally represented by time-uncorrelated white noise in the classical-LIM framework, but does so using the same observational dataset without requiring additional data. Furthermore, we show that colored LIM does not reduce to classical LIM in the white noise limit, underscoring the importance of temporal dependencies in stochastic systems. In this paper, we rigorously develop the colored LIM, explore its connections with the classical LIM, dynamic mode decomposition, and vector autoregressive moving average models, and validate its effectiveness on both ideal linear and nonlinear systems. In addition, we illustrate the potential applications and implications of colored LIM for real-world problems, including the El Niño–southern oscillation and the electricity network of Tohoku University. |
| format | Article |
| id | doaj-art-d62c0fb7937e4a5b85372f7e5ed05367 |
| institution | DOAJ |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-d62c0fb7937e4a5b85372f7e5ed053672025-08-20T03:14:20ZengAmerican Physical SocietyPhysical Review Research2643-15642025-04-017202304210.1103/PhysRevResearch.7.023042Colored linear inverse model: A data-driven method for studying dynamical systems with temporally correlated stochasticityJustin LienYan-Ning KuoHiroyasu AndoShoichiro KidoIn real-world problems, environmental noise is often idealized as Gaussian white noise, despite potential temporal dependencies. The linear inverse model (LIM) is a class of data-driven methods that extract dynamic and stochastic information from finite time-series data of complex systems. In this study, we introduce a new variant of LIM, called colored LIM, which models stochasticity using Ornstein-Uhlenbeck colored noise. Despite the nontrivial correlation between observable and colored noise, we show that colored LIM unveils the desired information merely from the correlation function of the observable. Therefore, this approach not only accounts for the memory effects of environmental noise, traditionally represented by time-uncorrelated white noise in the classical-LIM framework, but does so using the same observational dataset without requiring additional data. Furthermore, we show that colored LIM does not reduce to classical LIM in the white noise limit, underscoring the importance of temporal dependencies in stochastic systems. In this paper, we rigorously develop the colored LIM, explore its connections with the classical LIM, dynamic mode decomposition, and vector autoregressive moving average models, and validate its effectiveness on both ideal linear and nonlinear systems. In addition, we illustrate the potential applications and implications of colored LIM for real-world problems, including the El Niño–southern oscillation and the electricity network of Tohoku University.http://doi.org/10.1103/PhysRevResearch.7.023042 |
| spellingShingle | Justin Lien Yan-Ning Kuo Hiroyasu Ando Shoichiro Kido Colored linear inverse model: A data-driven method for studying dynamical systems with temporally correlated stochasticity Physical Review Research |
| title | Colored linear inverse model: A data-driven method for studying dynamical systems with temporally correlated stochasticity |
| title_full | Colored linear inverse model: A data-driven method for studying dynamical systems with temporally correlated stochasticity |
| title_fullStr | Colored linear inverse model: A data-driven method for studying dynamical systems with temporally correlated stochasticity |
| title_full_unstemmed | Colored linear inverse model: A data-driven method for studying dynamical systems with temporally correlated stochasticity |
| title_short | Colored linear inverse model: A data-driven method for studying dynamical systems with temporally correlated stochasticity |
| title_sort | colored linear inverse model a data driven method for studying dynamical systems with temporally correlated stochasticity |
| url | http://doi.org/10.1103/PhysRevResearch.7.023042 |
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