58 citations · 197 across the 46 of their papers we have counts for
7 papers · 1 filter
Path-Integral Formula for Computing Koopman Eigenfunctions
Shankar A. Deka, Sriram S. K. S. Narayanan, Umesh Vaidya
The paper is about the computation of the principal spectrum of the Koopman operator (i.e., eigenvalues and eigenfunctions). The principal eigenfunctions of the Koopman operator ar…
On Few Shot Learning of Dynamical Systems: A Koopman Operator Theoretic Approach
Subhrajit Sinha, Umesh Vaidya, Enoch Yeung
In this paper, we propose a novel algorithm for learning the Koopman operator of a dynamical system from a \textit{small} amount of training data. In many applications of data-driv…
On Computation of Koopman Operator from Sparse Data
Subhrajit Sinha, Enoch Yeung
In this paper we propose a novel approach to compute the Koopman operator from sparse time series data. In recent years there has been considerable interests in operator theoretic…
Data-Driven Approximation of Transfer Operators: Naturally Structured Dynamic Mode Decomposition
Bowen Huang, Umesh Vaidya
In this paper, we provide a new algorithm for the finite dimensional approximation of the linear transfer Koopman and Perron-Frobenius operator from time series data. We argue that…
Limitations for nonlinear stabilization over uncertain channels
Umesh Vaidya, Nicola Elia
We study the problem of mean-square exponential incremental stabilization of nonlinear systems over uncertain communication channels. We show the ability to stabilize a system over…
Stochastic Stability Analysis of Discrete Time System Using Lyapunov Measure
Umesh Vaidya
In this paper, we study the stability problem of a stochastic, nonlinear, discrete-time system. We introduce a linear transfer operator-based Lyapunov measure as a new tool for sta…
Existence of invariant tori in three dimensional maps with degeneracy
Umesh Vaidya, Igor Mezic
We prove a KAM-type result for the persistence of two-dimensional invariant tori in perturbations of integrable action-angle-angle maps with degeneracy, satisfying the intersection…