no code implementations • 21 Nov 2023 • William T. Redman, DeAn Huang, Maria Fonoberova, Igor Mezić
We find that a basic implementation of Koopman learning with episodic memory leads to significant improvements in prediction on synthetic and real-world data.
1 code implementation • 17 Feb 2023 • William T. Redman, Juan M. Bello-Rivas, Maria Fonoberova, Ryan Mohr, Ioannis G. Kevrekidis, Igor Mezić
Study of the nonlinear evolution deep neural network (DNN) parameters undergo during training has uncovered regimes of distinct dynamical behavior.
no code implementations • 21 Dec 2020 • Ryan Mohr, Maria Fonoberova, Zlatko Drmač, Iva Manojlović, Igor Mezić
Hierarchical support vector regression (HSVR) models a function from data as a linear combination of SVR models at a range of scales, starting at a coarse scale and moving to finer scales as the hierarchy continues.
no code implementations • 21 Jun 2020 • Iva Manojlović, Maria Fonoberova, Ryan Mohr, Aleksandr Andrejčuk, Zlatko Drmač, Yannis Kevrekidis, Igor Mezić
We also show how using Koopman modes we can selectively prune the network to speed up the training procedure.
1 code implementation • 18 Oct 2017 • Milan Korda, Mihai Putinar, Igor Mezić
We also show how to compute, from measured data, the spectral projection on a given segment of the unit circle, allowing us to obtain a finite-dimensional approximation of the operator that explicitly takes into account the point and continuous parts of the spectrum.
Dynamical Systems Numerical Analysis Spectral Theory
1 code implementation • 3 Apr 2017 • Hassan Arbabi, Igor Mezić
We observe that KMD outperforms the Proper Orthogonal Decomposition in reconstruction of the flows with strong quasi-periodic components. c features are present in the flow.
Fluid Dynamics 37N10
1 code implementation • 21 Nov 2016 • Hassan Arbabi, Igor Mezić
We establish the convergence of a class of numerical algorithms, known as Dynamic Mode Decomposition (DMD), for computation of the eigenvalues and eigenfunctions of the infinite-dimensional Koopman operator.
Dynamical Systems 37M10, 37A30, 65P99, 37N10