11 papers
Kernel-Based LMI Approaches to Solving the Hamilton-Jacobi-Bellman Equation and Nonlinear Optimal Control
Boumediene Hamzi, Umesh Vaidya
We present a kernel-based linear matrix inequality (LMI) approach for the approximate solution of Hamilton--Jacobi--Bellman (HJB) equations arising in nonlinear optimal control. Th…
Dictionary learning for Kernel EDMD
Erik Lien Bolager, Boumediene Hamzi, Houman Owhadi +2
Studying nonlinear dynamical systems through their state space behavior can be challenging, and one possible alternative is to analyze them via their associated Koopman operator. T…
Adaptive Kernel Selection for Kernelized Diffusion Maps
Othmane Aboussaad, Adam Miraoui, Boumediene Hamzi +1
Selecting an appropriate kernel is a central challenge in kernel-based spectral methods. In \emph{Kernelized Diffusion Maps} (KDM), the kernel determines the accuracy of the RKHS e…
Time Series Correlations and Kolmogorov Complexity: A Hausdorff Dimension Perspective
Boumediene Hamzi, Marianne Clausel, Kamal Dingle +2
Spurious correlations are common in time-series analysis because simple, low-complexity patterns can produce high Pearson correlations even between unrelated series. We argue that…
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…
Kernel Methods for Stochastic Dynamical Systems with Application to Koopman Eigenfunctions: Feynman-Kac Representations and RKHS Approximation
Boumediene Hamzi, Houman Owhadi, Umesh Vaidya
We extend the unified kernel framework for transport equations and Koopman eigenfunctions, developed in previous work by the authors for deterministic systems, to stochastic differ…