85 citations · 302 across the 30 of their papers we have counts for
15 papers · 1 filter
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-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…
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…
Kernel Methods for the Approximation of the Eigenfunctions of the Koopman Operator
Jonghyeon Lee, Boumediene Hamzi, Boya Hou +3
The Koopman operator provides a linear framework to study nonlinear dynamical systems. Its spectra offer valuable insights into system dynamics, but the operator can exhibit both d…
Gaussian Processes simplify differential equations
Jonghyeon Lee, Boumediene Hamzi, Yannis Kevrekidis +1
In this paper we use Gaussian processes (kernel methods) to learn mappings between trajectories of distinct differential equations. Our goal is to simplify both the representation…
Data-driven cold starting of good reservoirs
Lyudmila Grigoryeva, Boumediene Hamzi, Felix P. Kemeth +4
Using short histories of observations from a dynamical system, a workflow for the post-training initialization of reservoir computing systems is described. This strategy is called…
Exploring simplicity bias in 1D dynamical systems
Kamaludin Dingle, Mohammad Alaskandarani, Boumediene Hamzi +1
Arguments inspired by algorithmic information theory predict an inverse relation between the probability and complexity of output patterns in a wide range of input-output maps. Thi…
Kernel-based approximation of the Koopman generator and Schrödinger operator
Stefan Klus, Feliks Nüske, Boumediene Hamzi
Many dimensionality and model reduction techniques rely on estimating dominant eigenfunctions of associated dynamical operators from data. Important examples include the Koopman op…
Dimensionality Reduction of Complex Metastable Systems via Kernel Embeddings of Transition Manifolds
Andreas Bittracher, Stefan Klus, Boumediene Hamzi +2
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems.…
Greedy Kernel Methods for Center Manifold Approximation
Bernard Haasdonk, Boumediene Hamzi, Gabriele Santin +1
For certain dynamical systems it is possible to significantly simplify the study of stability by means of the center manifold theory. This theory allows to isolate the complicated…
Approximation of Lyapunov Functions from Noisy Data
Peter Giesl, Boumediene Hamzi, Martin Rasmussen +1
Methods have previously been developed for the approximation of Lyapunov functions using radial basis functions. However these methods assume that the evolution equations are known…
Kernel Methods for Linear Discrete-Time Equations
Fritz Colonius, Boumediene Hamzi
Methods from learning theory are used in the state space of linear dynamical and control systems in order to estimate the system matrices. An application to stabilization via algeb…