  We propose a method for estimating the asymptotic phase and amplitude
functions of limit-cycle oscillators using observed time series data without
prior knowledge of their dynamical equations. The estimation is performed by
polynomial regression and can be solved as a convex optimization problem. The
validity of the proposed method is numerically illustrated by using
two-dimensional limit-cycle oscillators as examples. As an application, we
demonstrate data-driven fast entrainment with amplitude suppression using the
optimal periodic input derived from the estimated phase and amplitude
functions.
