4 papers · 1 filter
Sharp Computational Bounds for Spectral Types of Schrödinger Operators
Matthew J. Colbrook, George Coote
We prove sharp bounds for determining the spectral-type decomposition of Schrödinger operators in the spirit of Smale's program on the foundations of computation. For explicit one-…
Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation
George Coote, Matthew J. Colbrook
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; th…
Residual Pseudospectra Reveal a Physics-Informed Koopman Backbone for Tropical Pacific Variability and ENSO Prediction
Paula Lorenzo-Sanchez, Matthew J. Colbrook, Antonio Navarra
Tropical Pacific sea-surface-temperature (SST) variability spans interacting timescales, with the ENSO as its dominant interannual expression. Yet the dynamical structure organizin…
Trustworthy Koopman Operator Learning: Invariance Diagnostics and Error Bounds
Gustav Conradie, Nicolas Boullé, Jean-Christophe Loiseau +2
Koopman operator theory provides a global linear representation of nonlinear dynamics and underpins many data-driven methods. In practice, however, finite-dimensional feature space…