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math.NA2026
Kernel Methods for Some Transport Equations with Application to Learning Kernels for the Approximation of Koopman Eigenfunctions: A Unified Approach via Variational Methods, Green's Functions and the Method of Characteristics
Boumediene Hamzi, Houman Owhadi, Umesh Vaidya
We present a unified theoretical and computational framework for constructing reproducing kernels tailored to transport equations and adapted to Koopman eigenfunctions of nonlinear…
math.NA2026
Kernel Methods for the Construction of Certified Lyapunov Functions via Approximate Koopman Eigenfunctions
P. Giesl, S. Hafstein, B. Hamzi +4
We present a kernel-based methodology for constructing Lyapunov functions for nonlinear dynamical systems using approximate Koopman eigenfunctions. Our approach decomposes principa…
math.NA2025
Data-efficient Kernel Methods for Learning Hamiltonian Systems
Yasamin Jalalian, Mostafa Samir, Boumediene Hamzi +2
Hamiltonian dynamics describe a wide range of physical systems. As such, data-driven simulations of Hamiltonian systems are important for many scientific and engineering problems.…