ArticleJournal of the Royal Society, Interface2021
Challenges in dynamic mode decomposition.
Article in Journal of the Royal Society, Interface, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 12 papers.
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Who cites it
12 citing papers in PubMed.
- A novel spatiotemporal decomposition and identification of sparse equations for human brain deformation.Scientific reports · 2026Article
- Sleep bruxism: a novel theoretical perspective through the lens of the free energy principle (FEP).Frontiers in behavioral neuroscience · 2026Article
- InputDSA : Demixing then comparing recurrent and externally driven dynamics.... International Conference on Learning Representations · 2026Article
- Article
- Data-driven identification of biological systems using multi-scale analysis.PLoS computational biology · 2025Article
- Membrane Interactions Drive Hydrogen-Bond Dynamics in the pH-Low Insertion Peptide (pHLIP).The journal of physical chemistry letters · 2025Article
- Dynamic mode decomposition for analysis and prediction of metabolic oscillations from time-lapse imaging of cellular autofluorescence.Scientific reports · 2025Article
- Machine learning on interictal intracranial EEG predicts surgical outcome in drug resistant epilepsy.NPJ digital medicine · 2025Article
- Enhancing spectral analysis in nonlinear dynamics with pseudoeigenfunctions from continuous spectra.Scientific reports · 2024Article
- Control of complex systems with generalized embedding and empirical dynamic modeling.PloS one · 2024Article
- Data-driven linearization of dynamical systems.Nonlinear dynamics · 2024Article
- Challenges in dynamic mode decomposition.Journal of the Royal Society, Interface · 2021Article
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Authors and funding
3 authors.
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Abstract
Dynamic mode decomposition (DMD) is a powerful tool for extracting spatial and temporal patterns from multi-dimensional time series, and it has been used successfully in a wide range of fields, including fluid mechanics, robotics and neuroscience. Two of the main challenges remaining in DMD research are noise sensitivity and issues related to Krylov space closure when modelling nonlinear systems. Here, we investigate the combination of noise and nonlinearity in a controlled setting, by studying a class of systems with linear latent dynamics which are observed via multinomial observables. Our numerical models include system and measurement noise. We explore the influences of dataset metrics, the spectrum of the latent dynamics, the normality of the system matrix and the geometry of the dynamics. Our results show that even for these very mildly nonlinear conditions, DMD methods often fail to recover the spectrum and can have poor predictive ability. Our work is motivated by our experience modelling multilegged robot data, where we have encountered great difficulty in reconstructing time series for oscillatory systems with intermediate transients, which decay only slightly faster than a period.
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