  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-driven modeling, e.g. biological network modeling,
cybersecurity, modeling the Internet of Things, or smart grid monitoring, it is
impossible to obtain regularly sampled time-series data with a sufficiently
high sampling frequency. In such situations the existing Dynamic Mode
Decomposition (DMD) or Extended Dynamic Mode Decomposition (EDMD) algorithms
for Koopman operator computation often leads to a low fidelity approximate
Koopman operator. To this end, this paper proposes an algorithm which can
compute the Koopman operator efficiently when the training data-set is sparsely
sampled across time. In particular, the proposed algorithm enriches the small
training data-set by appending artificial data points, which are treated as
noisy observations. The larger, albeit noisy data-set is then used to compute
the Koopman operator, using techniques from Robust Optimization. The efficacy
of the proposed algorithm is also demonstrated on three different dynamical
systems, namely a linear network of oscillators, a nonlinear system and a
dynamical system governed by a Partial Differential Equation (PDE).
