  We study the relaxation of a highly collisional, ultracold but nondegenerate
gas of polar molecules. Confined within a harmonic trap, the gas is subject to
fluid-gaseous coupled dynamics that lead to a breakdown of first-order
hydrodynamics. An attempt to treat these higher-order hydrodynamic effects was
previously made with a Gaussian ansatz and coarse-graining model parameter [R.
R. W. Wang & J. L. Bohn, Phys. Rev. A 108, 013322 (2023)], leading to an
approximate set of equations for a few collective observables accessible to
experiments. Here we present substantially improved reduced-order models for
these same observables, admissible beyond previous parameter regimes,
discovered directly from particle simulations using the WSINDy algorithm
(Weak-form Sparse Identification of Nonlinear Dynamics). The interpretable
nature of the learning algorithm enables estimation of previously unknown
physical quantities and discovery of model terms with candidate physical
mechanisms, revealing new physics in mixed collisional regimes. Our approach
constitutes a general framework for data-driven model identification leveraging
known physics.
