9 papers · 1 filter
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…
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 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…
A Dynamics-Informed Gaussian Process Framework for 2D Stochastic Navier-Stokes via Quasi-Gaussianity
Boumediene Hamzi, Houman Owhadi
The recent proof of quasi-Gaussianity for the 2D stochastic Navier--Stokes (SNS) equations by Coe, Hairer, and Tolomeo establishes that the system's unique invariant measure is equ…
Retrodicting Chaotic Systems: An Algorithmic Information Theory Approach
Kamal Dingle, Boumediene Hamzi, Marcus Hutter +1
Making accurate inferences about data is a key task in science and mathematics. Here we study the problem of \emph{retrodiction}, inferring past values of a series, in the context…