  Dispersion curves characterize the frequency dependence of the phase and the
group velocities of propagating elastic waves. Many analytical and numerical
techniques produce dispersion curves from physics-based models. However, it is
often challenging to accurately model engineering structures with intricate
geometric features and inhomogeneous material properties. For such cases, this
paper proposes a novel method to estimate group velocities from experimental
data-driven models. Experimental frequency response functions (FRFs) are used
to develop data-driven models, {which are then used to estimate dispersion
curves}. The advantages of this approach over other traditionally used
transient techniques stem from the need to conduct only steady-state
experiments. In comparison, transient experiments often need a higher-sampling
rate for wave-propagation applications and are more susceptible to noise.
  The vector-fitting (VF) algorithm is adopted to develop data-driven models
from experimental in-plane and out-of-plane FRFs of a one-dimensional
structure. The quality of the corresponding data-driven estimates is evaluated
using an analytical Timoshenko beam as a baseline. The data-driven model (using
the out-of-plane FRFs) estimates the anti-symmetric ($A_0$) group velocity with
a maximum error of $4\%$ over a 40~kHz frequency band. In contrast, group
velocities estimated from transient experiments resulted in a maximum error of
$6\%$ over the same frequency band.
