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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.11116 |
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| _version_ | 1866911379440533504 |
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| author | Nakamura, Yuki Takemoto, Shingo Ono, Shunsuke |
| author_facet | Nakamura, Yuki Takemoto, Shingo Ono, Shunsuke |
| contents | We propose Comprehensive Robust Dynamic Mode Decomposition (CR-DMD), a novel framework that robustifies the entire DMD process - from mode extraction to dimensional reduction - against mixed noise. Although standard DMD widely used for uncovering spatio-temporal patterns and constructing low-dimensional models of dynamical systems, it suffers from significant performance degradation under noise due to its reliance on least-squares estimation for computing the linear time evolution operator. Existing robust variants typically modify the least-squares formulation, but they remain unstable and fail to ensure faithful low-dimensional representations. First, we introduce a convex optimization-based preprocessing method designed to effectively remove mixed noise, achieving accurate and stable mode extraction. Second, we propose a new convex formulation for dimensional reduction that explicitly links the robustly extracted modes to the original noisy observations, constructing a faithful representation of the original data via a sparse weighted sum of the modes. Both stages are efficiently solved by a preconditioned primal-dual splitting method. Experiments on fluid dynamics datasets demonstrate that CR-DMD consistently outperforms state-of-the-art robust DMD methods in terms of mode accuracy and fidelity of low-dimensional representations under noisy conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11116 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Comprehensive Robust Dynamic Mode Decomposition from Mode Extraction to Dimensional Reduction Nakamura, Yuki Takemoto, Shingo Ono, Shunsuke Signal Processing Machine Learning We propose Comprehensive Robust Dynamic Mode Decomposition (CR-DMD), a novel framework that robustifies the entire DMD process - from mode extraction to dimensional reduction - against mixed noise. Although standard DMD widely used for uncovering spatio-temporal patterns and constructing low-dimensional models of dynamical systems, it suffers from significant performance degradation under noise due to its reliance on least-squares estimation for computing the linear time evolution operator. Existing robust variants typically modify the least-squares formulation, but they remain unstable and fail to ensure faithful low-dimensional representations. First, we introduce a convex optimization-based preprocessing method designed to effectively remove mixed noise, achieving accurate and stable mode extraction. Second, we propose a new convex formulation for dimensional reduction that explicitly links the robustly extracted modes to the original noisy observations, constructing a faithful representation of the original data via a sparse weighted sum of the modes. Both stages are efficiently solved by a preconditioned primal-dual splitting method. Experiments on fluid dynamics datasets demonstrate that CR-DMD consistently outperforms state-of-the-art robust DMD methods in terms of mode accuracy and fidelity of low-dimensional representations under noisy conditions. |
| title | Comprehensive Robust Dynamic Mode Decomposition from Mode Extraction to Dimensional Reduction |
| topic | Signal Processing Machine Learning |
| url | https://arxiv.org/abs/2601.11116 |