# Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantification arXiv: https://arxiv.org/abs/2107.10878 ยท HTML: https://mlsanity.com/paper/2107.10878/ ## Key facts - Cited by 30 papers in the map (data through 14 Oct 2026). - Builds on 9 of its 59 references that are in the map. - First posted on arXiv 22 Jul 2021. ## Builds on (most cited first, 9 of 9) - [Towards Understanding Ensemble, Knowledge Distillation and Self-Distillation in Deep Learning](https://mlsanity.com/paper/2012.09816/) (2020) - [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014) - [From Fourier to Koopman: Spectral Methods for Long-term Time Series Prediction](https://mlsanity.com/paper/2004.00574/) (2020) - [Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition](https://mlsanity.com/paper/1409.5496/) (2014) - [Sparsity-promoting dynamic mode decomposition](https://mlsanity.com/paper/1309.4165/) (2013) - [Compressed Dynamic Mode Decomposition for Background Modeling](https://mlsanity.com/paper/1512.04205/) (2015) - [Derivative-Based Koopman Operators for Real-Time Control of Robotic Systems](https://mlsanity.com/paper/2010.05778/) (2020) - [Randomized Matrix Decompositions using R](https://mlsanity.com/paper/1608.02148/) (2016) - [Dynamic Mode Decomposition for Real-Time Background/Foreground Separation in Video](https://mlsanity.com/paper/1404.7592/) (2014) ## Built on by (most cited first, 30 of 30) - [Discrepancy Modeling Framework: Learning missing physics, modeling systematic residuals, and disambiguating between deterministic and random effects](https://mlsanity.com/paper/2203.05164/) (2022) - [Shallow Recurrent Decoder for Reduced Order Modeling of Plasma Dynamics](https://mlsanity.com/paper/2405.11955/) (2024) - [Dynamic Mode Decomposition for data-driven analysis and reduced-order modelling of ExB plasmas: I. Extraction of spatiotemporally coherent patterns](https://mlsanity.com/paper/2308.13726/) (2023) - [Dynamic Mode Decomposition for data-driven analysis and reduced-order modelling of ExB plasmas: II. dynamics forecasting](https://mlsanity.com/paper/2308.13727/) (2023) - [The Seismic Wavefield Common Task Framework](https://mlsanity.com/paper/2512.19927/) (2025) - [Data-driven local operator finding for reduced-order modelling of plasma systems: I. Concept and verifications](https://mlsanity.com/paper/2403.01523/) (2024) - [Data-driven local operator finding for reduced-order modelling of plasma systems: II. Application to parametric dynamics](https://mlsanity.com/paper/2403.01532/) (2024) - [Towards Efficient Parametric State Estimation in Circulating Fuel Reactors with Shallow Recurrent Decoder Networks](https://mlsanity.com/paper/2503.08904/) (2025) - [Machine Learning Applications to Computational Plasma Physics and Reduced-Order Plasma Modeling: A Perspective](https://mlsanity.com/paper/2409.02349/) (2024) - [T-SHRED: Symbolic Regression for Regularization and Model Discovery with Transformer Shallow Recurrent Decoders](https://mlsanity.com/paper/2506.15881/) (2025) - [Trustworthy Koopman Operator Learning: Invariance Diagnostics and Error Bounds](https://mlsanity.com/paper/2603.15091/) (2026) - [A case study of spatiotemporal forecasting techniques for weather forecasting](https://mlsanity.com/paper/2209.14782/) (2022) - [Coupled and Uncoupled Dynamic Mode Decomposition in Multi-Compartmental Systems with Applications to Epidemiological and Additive Manufacturing Problems](https://mlsanity.com/paper/2110.06375/) (2021) - [Enhancing Dynamic Mode Decomposition Workflow with In-Situ Visualization and Data Compression](https://mlsanity.com/paper/2208.07767/) (2022) - [LINOCS: Lookahead Inference of Networked Operators for Continuous Stability](https://mlsanity.com/paper/2404.18267/) (2024) - [A Comparison of Parametric Dynamic Mode Decomposition Algorithms for Thermal-Hydraulics Applications](https://mlsanity.com/paper/2503.24205/) (2025) - [Factorized Neural Implicit DMD for Parametric Dynamics](https://mlsanity.com/paper/2603.10995/) (2026) - [Variational Mode Decomposition-Based Nonstationary Coherent Structure Analysis for Spatiotemporal Data](https://mlsanity.com/paper/2312.12113/) (2023) - [Optimized Dynamic Mode Decomposition for Reconstruction and Forecasting of Atmospheric Chemistry Data](https://mlsanity.com/paper/2404.12396/) (2024) - [Discovery and inversion of the viscoelastic wave equation in inhomogeneous media](https://mlsanity.com/paper/2409.18370/) (2024) - [Parsimonious Dynamic Mode Decomposition: A Robust and Automated Approach for Optimally Sparse Mode Selection in Complex Systems](https://mlsanity.com/paper/2410.16656/) (2024) - [Multiscale autonomous forecasting of plasma systems' dynamics using neural networks](https://mlsanity.com/paper/2502.11203/) (2025) - [Augmented Physics-Based Li-ion Battery Model via Adaptive Ensemble Sparse Learning and Conformal Prediction](https://mlsanity.com/paper/2507.00353/) (2025) - [Sparse-mode Dynamic Mode Decomposition for Disambiguating Local and Global Structures](https://mlsanity.com/paper/2507.19787/) (2025) - [System Identification of a Moored ASV with Recessed Moon Pool via Deterministic and Bayesian Hankel-DMDc](https://mlsanity.com/paper/2511.03482/) (2025) - [Data-driven uncertainty-aware seakeeping prediction of the Delft 372 catamaran using ensemble Hankel dynamic mode decomposition](https://mlsanity.com/paper/2511.04461/) (2025) - [Sparse-to-Field Reconstruction via Stochastic Neural Dynamic Mode Decomposition](https://mlsanity.com/paper/2511.20612/) (2025) - [Comprehensive Robust Dynamic Mode Decomposition from Mode Extraction to Dimensional Reduction](https://mlsanity.com/paper/2601.11116/) (2026) - [An Interpretable Data-Driven Model of the Flight Dynamics of Hawks](https://mlsanity.com/paper/2602.19196/) (2026) - [A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems](https://mlsanity.com/paper/2606.13063/) (2026) ## Abstract (arXiv) Dynamic mode decomposition (DMD) provides a regression framework for adaptively learning a best-fit linear dynamics model over snapshots of temporal, or spatio-temporal, data. A diversity of regression techniques have been developed for producing the linear model approximation whose solutions are exponentials in time. For spatio-temporal data, DMD provides low-rank and interpretable models in the form of dominant modal structures along with their exponential/oscillatory behavior in time. The majority of DMD algorithms, however, 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. Here, the optimized DMD algorithm is improved by using statistical bagging methods whereby a single set of snapshots is used to produce an ensemble of optimized DMD models. The outputs of these models are averaged to produce a bagging, optimized dynamic mode decomposition (BOP-DMD). BOP-DMD not only improves performance, it also robustifies the model and provides both spatial and temporal uncertainty quantification (UQ). Thus unlike currently available DMD algorithms, BOP-DMD provides a stable and robust model for probabilistic, or Bayesian forecasting with comprehensive UQ metrics.