Comprehensive Robust Dynamic Mode Decomposition from Mode Extraction to Dimensional Reduction
This addresses the issue of noise sensitivity in DMD for dynamical systems analysis, offering improved robustness, but it is incremental as it builds on existing robust variants.
The authors tackled the problem of Dynamic Mode Decomposition (DMD) performance degradation under mixed noise by proposing CR-DMD, a framework that robustifies mode extraction and dimensional reduction, resulting in consistent outperformance over state-of-the-art methods in accuracy and fidelity on fluid dynamics datasets.
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.