On the Cyclostationary Linear Inverse Models: A Mathematical Insight and Implication
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866918004877426688 |
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| author | Lien, Justin Kuo, Yan-Ning Ando, Hiroyasu |
| author_facet | Lien, Justin Kuo, Yan-Ning Ando, Hiroyasu |
| contents | Cyclostationary linear inverse models (CS-LIMs), generalized versions of the classical (stationary) LIM, are advanced data-driven techniques for extracting the first-order time-dependent dynamics and random forcing relevant information from complex non-linear stochastic processes. Though CS-LIMs lead to a breakthrough in climate sciences, their mathematical background and properties are worth further exploration. This study focuses on the mathematical perspective of CS-LIMs and introduces two variants: e-CS-LIM and l-CS-LIM. The former refines the original CS-LIM using the interval-wise linear Markov approximation, while the latter serves as an analytic inverse model for the linear periodic stochastic systems. Although relying on approximation, e-CS-LIM converges to l-CS-LIM under specific conditions and shows noise-robust performance. Numerical experiments demonstrate that each CS-LIM reveals the temporal structure of the system. The e-CS-LIM optimizes the original model for better dynamics performance, while l-CS-LIM excels in diffusion estimation due to reduced approximation reliance. Moreover, CS-LIMs are applied to real-world ENSO data, yielding a consistent result aligning with observations and current ENSO understanding. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10931 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Cyclostationary Linear Inverse Models: A Mathematical Insight and Implication Lien, Justin Kuo, Yan-Ning Ando, Hiroyasu Numerical Analysis Cyclostationary linear inverse models (CS-LIMs), generalized versions of the classical (stationary) LIM, are advanced data-driven techniques for extracting the first-order time-dependent dynamics and random forcing relevant information from complex non-linear stochastic processes. Though CS-LIMs lead to a breakthrough in climate sciences, their mathematical background and properties are worth further exploration. This study focuses on the mathematical perspective of CS-LIMs and introduces two variants: e-CS-LIM and l-CS-LIM. The former refines the original CS-LIM using the interval-wise linear Markov approximation, while the latter serves as an analytic inverse model for the linear periodic stochastic systems. Although relying on approximation, e-CS-LIM converges to l-CS-LIM under specific conditions and shows noise-robust performance. Numerical experiments demonstrate that each CS-LIM reveals the temporal structure of the system. The e-CS-LIM optimizes the original model for better dynamics performance, while l-CS-LIM excels in diffusion estimation due to reduced approximation reliance. Moreover, CS-LIMs are applied to real-world ENSO data, yielding a consistent result aligning with observations and current ENSO understanding. |
| title | On the Cyclostationary Linear Inverse Models: A Mathematical Insight and Implication |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2407.10931 |