12 citations · 15 across the 4 of their papers we have counts for
6 papers
Learning Kolmogorov Backward Operators for Spectral Analysis and Forecasting: A Data-Driven Variational Galerkin Framework
Yuanchao Xu, Claire Valva, Ben Gao +1
For a time-homogeneous Markov process, the fixed-lag solution operator \( (T_τf)(x)=\mathbb E[f(X_{t+τ})\mid X_t=x] \) of the Kolmogorov backward equation evolves observables linea…
A more predictable Madden-Julian Oscillation index derived from Koopman spectral analysis
Claire Valva, Edwin P. Gerber
The Madden-Julian oscillation (MJO) is a major source of subseasonal-to-seasonal (S2S) predictability. The MJO is commonly defined and tracked with indices such as the Real-time Mu…
Physics-informed spectral approximation of Koopman operators
Claire Valva, Dimitrios Giannakis
Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This fra…
The QBO, the annual cycle, and their interactions: Isolating periodic modes with Koopman analysis
Claire Valva, Edwin P. Gerber
The Quasi-Biennial Oscillation (QBO) is the dominant mode of variability in the equatorial stratosphere. It is characterized by alternating descending easterly and westerly jets ov…
Consistent spectral approximation of Koopman operators using resolvent compactification
Claire Valva, Dimitrios Giannakis
Koopman operators and transfer operators represent dynamical systems through their induced linear action on vector spaces of observables, enabling the use of operator-theoretic tec…
Koopman analysis of the periodic Korteweg-de Vries equation
Jeremy P Parker, Claire Valva
The eigenspectrum of the Koopman operator enables the decomposition of nonlinear dynamics into a sum of nonlinear functions of the state space with purely exponential and sinusoida…