The spatiotemporal coupling in delay-coordinates dynamic mode decomposition
Bibliographic record
Abstract
Dynamic mode decomposition (DMD) is a leading tool for equation-free analysis of high-dimensional dynamical systems from observations. In this work, we focus on a combination of DMD and delay-coordinates embedding, which is termed delay-coordinates DMD and is based on augmenting observations from current and past time steps, accommodating the analysis of a broad family of observations. An important utility of DMD is the compact and reduced-order spectral representation of observations in terms of the DMD eigenvalues and modes, where the temporal information is separated from the spatial information. From a spatiotemporal viewpoint, we show that when DMD is applied to delay-coordinates embedding, temporal information is intertwined with spatial information, inducing a particular spectral structure on the DMD components. We formulate and analyze this structure, which we term the spatiotemporal coupling in delay-coordinates DMD. Based on this spatiotemporal coupling, we propose a new method for DMD components selection. When using delay-coordinates DMD that comprises redundant modes, this selection is an essential step for obtaining a compact and reduced-order representation of the observations. We demonstrate our method on noisy simulated signals and various dynamical systems and show superior component selection compared to a commonly used method that relies on the amplitudes of the modes.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".