On cyclostationary linear inverse models: a mathematical insight and implication
Cyclostationary linear inverse models (CS-LIMs) are advanced data-driven techniques for extracting first-order time-dependent dynamics and random forcing information from cyclostationary observational data. This study focuses on the mathematical perspective of CS-LIMs and presents two variants, name...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Frontiers Media S.A.
2025-04-01
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| Series: | Frontiers in Complex Systems |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/articles/10.3389/fcpxs.2025.1563687/full |
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| Summary: | Cyclostationary linear inverse models (CS-LIMs) are advanced data-driven techniques for extracting first-order time-dependent dynamics and random forcing information from cyclostationary observational data. This study focuses on the mathematical perspective of CS-LIMs and presents two variants, namely, e-CS-LIM and l-CS-LIM. The e-CS-LIM, improved from the original CS-LIM, constructs the first-order dynamics through the interval-wise application of the stationary LIM (ST-LIM), capturing the integrated effect of each interval where similar cyclostationary dependencies are present. This approach provides robustness against noise but is affected by the Nyquist issue, similar to the ST-LIM. The l-CS-LIM, on the other hand, estimates the time-dependent Jacobian of the underlying system. Although more sensitive to noise, this method is free from the Nyquist issue. Numerical experiments demonstrate that both CS-LIM variants effectively capture the temporal structure of the underlying system using synthetic observational data. Moreover, when applied to real-world ENSO data, CS-LIMs yield consistent results that align well with the observations and current El Niño–Southern Oscillation (ENSO) understanding. |
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| ISSN: | 2813-6187 |