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math.DS2026
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…
math.DS2024
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…
math.DS2023★ 12 cited
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…