Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation
Koopman theory promises linear structure in nonlinear dynamics, but numerical Koopman spectra are easy to compute and hard to trust. A finite EDMD matrix always has eigenvalues; the problem is that many of them may have nothing to do with the infinite-dimensional operator. In this paper we make spectral reliability the objective of dictionary learning. We train neural-network dictionaries not merely to predict the next snapshot, but to minimize Residual Dynamic Mode Decomposition residuals: operator-level a posteriori errors that test whether computed eigenvalues and modes are genuine Koopman spectral objects. To keep the learned observables from collapsing into an unstable coordinate sys...
| Authors | George Coote, Matthew J. Colbrook |
|---|---|
| Primary category | math.NA |
| Published | 27 June 2026 |
| Last updated at source | 27 June 2026 |
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