Seminar: Graduate Seminar
Robust Order Detection in Delay-Coordinate Dynamic Mode Decomposition via Mode Structure
Date:
February,04,2026
Start Time:
13:30 - 14:30
Location:
506, Zisapel Building
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Lecturer:
Yoav Harris
Research Areas:
| High-dimensional (multivariate) time-series often arise from complex systems whose underlying dynamics are low-dimensional but observed through many coupled measurements. Dynamic Mode Decomposition (DMD) is a widely used data-driven tool that decomposes the evolution into temporal trajectories and associated spatial patterns (modes). In practice, a core bottleneck is order detection: deciding how many modes reflect true dynamics versus artifacts. This becomes especially acute with delay coordinates (delay-embedded DMD), where common eigenvalue- and energy-based heuristics can fail as the embedding length grows. We provide a purely-data-driven estimate of how each mode aligns with the unknown signal subspace. This Estimated-Subspace-Residual (ESR) reliably separates true and spurious modes. We also study the internal structure of modes in delay embeddings, showing that both the emergence of structured spurious components and their deviations are governed by the same ESR geometry. Based on this understanding, we develop improved geometric and structural criteria for robust mode selection. Across extensive numerical experiments (simulations) and a range of baselines, our methods consistently outperform existing alternatives in order detection and mode identification, in delay-coordinate DMD and, where applicable, in standard (non-delay) DMD. |
| M.Sc. student under the supervision of Prof. Ronen Talmon (ECE), Dr. Hadas Benisty (Medicine).
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