Iterative Sparse Identification of Nonlinear Dynamics
In order to extract governing equations from time-series data, various approaches are proposed. Among those, sparse identification of nonlinear dynamics (SINDy) stands out as a successful method capable of modeling governing equations with a minimal number of terms, utilizing the principles of compr...
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2024-01-01
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| Series: | IEEE Open Journal of Signal Processing |
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| Online Access: | https://ieeexplore.ieee.org/document/10750024/ |
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| author | Jinho Choi |
| author_facet | Jinho Choi |
| author_sort | Jinho Choi |
| collection | DOAJ |
| description | In order to extract governing equations from time-series data, various approaches are proposed. Among those, sparse identification of nonlinear dynamics (SINDy) stands out as a successful method capable of modeling governing equations with a minimal number of terms, utilizing the principles of compressive sensing. This feature, which relies on a small number of terms, is crucial for interpretability. The effectiveness of SINDy hinges on the choice of candidate functions within its dictionary to extract governing equations of dynamical systems. A larger dictionary allows for more terms, enhancing the quality of approximations. However, the computational complexity scales with dictionary size, rendering SINDy less suitable for high-dimensional datasets, even though it has been successfully applied to low-dimensional datasets. To address this challenge, we introduce iterative SINDy in this paper, where the dictionary undergoes expansion and compression through iterations. We also conduct an analysis of the convergence properties of iterative SINDy. Simulation results validate that iterative SINDy can achieve nearly identical performance to SINDy, while significantly reducing computational complexity. Notably, iterative SINDy demonstrates effectiveness with high-dimensional time-series data without incurring the prohibitively high computational cost associated with SINDy. |
| format | Article |
| id | doaj-art-ebf47673900f49da990956f756a19abc |
| institution | OA Journals |
| issn | 2644-1322 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Open Journal of Signal Processing |
| spelling | doaj-art-ebf47673900f49da990956f756a19abc2025-08-20T02:01:57ZengIEEEIEEE Open Journal of Signal Processing2644-13222024-01-0151107111810.1109/OJSP.2024.349555310750024Iterative Sparse Identification of Nonlinear DynamicsJinho Choi0https://orcid.org/0000-0002-4895-6680School of Electrical and Mechanical Engineering, The University of Adelaide, Adelaide, SA, AustraliaIn order to extract governing equations from time-series data, various approaches are proposed. Among those, sparse identification of nonlinear dynamics (SINDy) stands out as a successful method capable of modeling governing equations with a minimal number of terms, utilizing the principles of compressive sensing. This feature, which relies on a small number of terms, is crucial for interpretability. The effectiveness of SINDy hinges on the choice of candidate functions within its dictionary to extract governing equations of dynamical systems. A larger dictionary allows for more terms, enhancing the quality of approximations. However, the computational complexity scales with dictionary size, rendering SINDy less suitable for high-dimensional datasets, even though it has been successfully applied to low-dimensional datasets. To address this challenge, we introduce iterative SINDy in this paper, where the dictionary undergoes expansion and compression through iterations. We also conduct an analysis of the convergence properties of iterative SINDy. Simulation results validate that iterative SINDy can achieve nearly identical performance to SINDy, while significantly reducing computational complexity. Notably, iterative SINDy demonstrates effectiveness with high-dimensional time-series data without incurring the prohibitively high computational cost associated with SINDy.https://ieeexplore.ieee.org/document/10750024/Nonlinear dynamicscompressive sensingsparse identification of nonlinear dynamics (SINDy) |
| spellingShingle | Jinho Choi Iterative Sparse Identification of Nonlinear Dynamics IEEE Open Journal of Signal Processing Nonlinear dynamics compressive sensing sparse identification of nonlinear dynamics (SINDy) |
| title | Iterative Sparse Identification of Nonlinear Dynamics |
| title_full | Iterative Sparse Identification of Nonlinear Dynamics |
| title_fullStr | Iterative Sparse Identification of Nonlinear Dynamics |
| title_full_unstemmed | Iterative Sparse Identification of Nonlinear Dynamics |
| title_short | Iterative Sparse Identification of Nonlinear Dynamics |
| title_sort | iterative sparse identification of nonlinear dynamics |
| topic | Nonlinear dynamics compressive sensing sparse identification of nonlinear dynamics (SINDy) |
| url | https://ieeexplore.ieee.org/document/10750024/ |
| work_keys_str_mv | AT jinhochoi iterativesparseidentificationofnonlineardynamics |