  Two-dimensional active nematics are often modeled using phenomenological
continuum theories that describe the dynamics of the nematic director and fluid
velocity through partial differential equations (PDEs). While these models
provide a statistically accurate description of the experiments, the
identification of the relevant terms in the PDEs and their parameters is
usually indirect. Here, we adapt a recently developed method to automatically
identify optimal continuum models for active nematics directly from the
spatio-temporal director and velocity data, via sparse fitting of the
coarse-grained fields onto generic low order PDEs. We test the method
extensively on computational models, and then apply it to data from experiments
on microtubule-based active nematics. Thereby, we identify the optimal models
for microtubule-based active nematics, along with the relevant phenomenological
parameters. We find that the dynamics of the orientation field are largely
governed by its coupling to the underlying flow, with free-energy gradients
playing a negligible role. Furthermore, by fitting the flow equation to
experimental data, we estimate a key parameter quantifying the `activity' of
the nematic.
