Comprehensive Robust Dynamic Mode Decomposition from Mode Extraction to Dimensional Reduction

2026-01-16

AI Summary

This work addresses the significant performance degradation of standard Dynamic Mode Decomposition (DMD) under mixed noise, which hinders accurate modal identification and high-fidelity low-dimensional representations. To overcome this limitation, the authors propose CR-DMD, a novel framework that robustifies the entire DMD pipeline for the first time. The approach integrates convex optimization-based preprocessing to suppress mixed noise, introduces a new convex optimization model for robust mode extraction, and explicitly links the reconstructed modes to the original observations to guide sparse weighted dimensionality reduction. An efficient preconditioned primal-dual splitting algorithm is employed to solve the resulting optimization problem. Experiments on fluid dynamics datasets demonstrate that CR-DMD substantially outperforms existing robust DMD methods in noisy environments, achieving markedly improved modal accuracy and fidelity of low-dimensional reconstructions.

Technology Category

• Machine Learning: Multimodal Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Computer Vision: Multi-modal Vision

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

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.

Problem

• Dynamic Mode Decomposition
• noise robustness
• low-dimensional representation
• mode extraction
• mixed noise

Innovation

• Robust Dynamic Mode Decomposition
• Convex Optimization
• Mixed Noise Removal
• Dimensionality Reduction
• Primal-Dual Splitting