  Reduced modeling of a computationally demanding dynamical system aims at
approximating its trajectories, while optimizing the trade-off between accuracy
and computational complexity. In this work, we propose to achieve such an
approximation by first embedding the trajectories in a reproducing kernel
Hilbert space (RKHS), which exhibits appealing approximation and computational
capabilities, and then solving the associated reduced model problem. More
specifically, we propose a new efficient algorithm for data-driven reduced
modeling of non-linear dynamics based on linear approximations in a RKHS. This
algorithm takes advantage of the closed-form solution of a low-rank constraint
optimization problem while exploiting advantageously kernel-based computations.
Reduced modeling with this algorithm reveals a gain in approximation accuracy,
as shown by numerical simulations, and in complexity with respect to existing
approaches.
