Physics-guided weak-form discovery of reduced-order models for trapped ultracold hydrodynamics
This work addresses the breakdown of first-order hydrodynamics in ultracold gas experiments, offering a data-driven framework for physicists, though it is incremental as it builds on prior Gaussian ansatz methods.
The authors tackled the problem of modeling higher-order hydrodynamic effects in trapped ultracold gases by developing improved reduced-order models using the WSINDy algorithm, which led to models valid beyond previous regimes and revealed new physics in mixed collisional regimes.
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.