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Predicting the Critical Number of Layers for Hierarchical Support Vector Regression
Ryan Mohr, Maria Fonoberova, Zlatko Drmač +2
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…
Koopman Operator, Geometry, and Learning
Igor Mezic
We provide a framework for learning of dynamical systems rooted in the concept of representations and Koopman operators. The interplay between the two leads to the full description…
On Numerical Approximations of the Koopman Operator
Igor Mezic
We study numerical approaches to computation of spectral properties of composition operators. We provide a characterization of Koopman Modes in Banach spaces using Generalized Lapl…
Koopman Resolvent: A Laplace-Domain Analysis of Nonlinear Autonomous Dynamical Systems
Yoshihiko Susuki, Alexandre Mauroy, Igor Mezic
The motivation of our research is to establish a Laplace-domain theory that provides principles and methodology to analyze and synthesize systems with nonlinear dynamics. A semigro…
Applications of Koopman Mode Analysis to Neural Networks
Iva Manojlović, Maria Fonoberova, Ryan Mohr +4
We consider the training process of a neural network as a dynamical system acting on the high-dimensional weight space. Each epoch is an application of the map induced by the optim…
Spectral Analysis of the Koopman Operator for Partial Differential Equations
Hiroya Nakao, Igor Mezić
We provide an overview of the Koopman operator analysis for a class of partial differential equations describing relaxation of the field variable to a stable stationary state. We i…