Comprehensive Robust Dynamic Mode Decomposition from Mode Extraction to Dimensional Reduction

• URL: http://arxiv.org/abs/2601.11116v1
• Date: Fri, 16 Jan 2026 09:21:56 GMT
• Title: Comprehensive Robust Dynamic Mode Decomposition from Mode Extraction to Dimensional Reduction
• Authors: Yuki Nakamura, Shingo Takemoto, Shunsuke Ono,
• Abstract summary: Comprehensive Dynamic Robust Mode Decomposition (CR-DMD) is a framework that robustifies the entire process.<n>CR-DMD consistently outperforms state-of-art robust DMD methods in terms of mode accuracy and fidelity of low-dimensional representations under noisy conditions.
• Score: 16.886493310057194
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

Related papers

• Sparse-mode Dynamic Mode Decomposition for Disambiguating Local and Global Structures [48.407500521383646]
  We introduce sparse-mode DMD, a new variant of the optimized DMD framework that leverages sparsity-temporal regularization.<n>The algorithm maintains the noise-robust of optimized modes while disambiguating between modes which are local versus global in nature.<n>We demonstrate this by analyzing synthetic and real-world systems, including examples from optical waveguides, quantum mechanics, and surface temperature data.
  arXiv  Detail & Related papers  (2025-07-26T04:24:40Z)
• Latent Mode Decomposition [0.3683202928838613]
  We introduce Variational Latent Mode Decomposition (VLMD), a new algorithm for extracting oscillatory modes from multivariate signals.<n>Its improved performance is driven by a novel underlying model, Latent Mode Decomposition (LMD), which blends sparse coding and mode decomposition.<n> Experiments on synthetic and real-world datasets demonstrate that VLMD outperforms state-of-the-art MMD methods in accuracy, efficiency, and interpretability.
  arXiv  Detail & Related papers  (2025-05-23T12:16:35Z)
• Parsimonious Dynamic Mode Decomposition: A Robust and Automated Approach for Optimally Sparse Mode Selection in Complex Systems [0.40964539027092917]
  This paper introduces the Parsimonious Dynamic Mode Decomposition (parsDMD)<n>ParsDMD is a novel algorithm designed to automatically select an optimally sparse subset of dynamic modes for both temporal and purely temporal data.<n>It is validated on a diverse range of datasets, including standing wave signals, identifying hidden dynamics, fluid dynamics simulations, and atmospheric sea-surface temperature (SST) data.
  arXiv  Detail & Related papers  (2024-10-22T03:00:11Z)
• AdjointDPM: Adjoint Sensitivity Method for Gradient Backpropagation of Diffusion Probabilistic Models [103.41269503488546]
  Existing customization methods require access to multiple reference examples to align pre-trained diffusion probabilistic models with user-provided concepts. This paper aims to address the challenge of DPM customization when the only available supervision is a differentiable metric defined on the generated contents. We propose a novel method AdjointDPM, which first generates new samples from diffusion models by solving the corresponding probability-flow ODEs. It then uses the adjoint sensitivity method to backpropagate the gradients of the loss to the models' parameters.
  arXiv  Detail & Related papers  (2023-07-20T09:06:21Z)
• Hierarchical Integration Diffusion Model for Realistic Image Deblurring [71.76410266003917]
  Diffusion models (DMs) have been introduced in image deblurring and exhibited promising performance. We propose the Hierarchical Integration Diffusion Model (HI-Diff), for realistic image deblurring. Experiments on synthetic and real-world blur datasets demonstrate that our HI-Diff outperforms state-of-the-art methods.
  arXiv  Detail & Related papers  (2023-05-22T12:18:20Z)
• Distributed Dynamic Safe Screening Algorithms for Sparse Regularization [73.85961005970222]
  We propose a new distributed dynamic safe screening (DDSS) method for sparsity regularized models and apply it on shared-memory and distributed-memory architecture respectively. We prove that the proposed method achieves the linear convergence rate with lower overall complexity and can eliminate almost all the inactive features in a finite number of iterations almost surely.
  arXiv  Detail & Related papers  (2022-04-23T02:45:55Z)
• Extension of Dynamic Mode Decomposition for dynamic systems with incomplete information based on t-model of optimal prediction [69.81996031777717]
  The Dynamic Mode Decomposition has proved to be a very efficient technique to study dynamic data. The application of this approach becomes problematic if the available data is incomplete because some dimensions of smaller scale either missing or unmeasured. We consider a first-order approximation of the Mori-Zwanzig decomposition, state the corresponding optimization problem and solve it with the gradient-based optimization method.
  arXiv  Detail & Related papers  (2022-02-23T11:23:59Z)
• Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantification [2.741266294612776]
  Dynamic mode decomposition (DMD) provides a framework for learning a best-fit linear dynamics model over snapshots of temporal, or-temporal, data. The majority of DMD algorithms are prone to bias errors from noisy measurements of the dynamics, leading to poor model fits and unstable forecasting capabilities. The optimized DMD algorithm minimizes the model bias with a variable projection optimization, thus leading to stabilized forecasting capabilities.
  arXiv  Detail & Related papers  (2021-07-22T18:14:20Z)
• Dynamic Mode Decomposition in Adaptive Mesh Refinement and Coarsening Simulations [58.720142291102135]
  Dynamic Mode Decomposition (DMD) is a powerful data-driven method used to extract coherent schemes. This paper proposes a strategy to enable DMD to extract from observations with different mesh topologies and dimensions.
  arXiv  Detail & Related papers  (2021-04-28T22:14:25Z)
• Unifying Theorems for Subspace Identification and Dynamic Mode Decomposition [6.735657356113614]
  We propose a SID-DMD algorithm that delivers a provably optimal model and that is easy to implement. We demonstrate our developments using a case study that aims to build dynamical models directly from video data.
  arXiv  Detail & Related papers  (2020-03-16T19:03:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.