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.

翻译：我们研究了高度碰撞、超冷但非简并的极性分子气体的弛豫过程。该气体被约束在谐振势阱中，其流体-气体耦合动力学导致了一阶流体动力学的失效。此前，研究者通过高斯假设和粗粒化模型参数尝试处理这些高阶流体动力学效应[R. R. W. Wang & J. L. Bohn, Phys. Rev. A 108, 013322 (2023)]，得到了针对若干可实验测量的集体可观测量的一组近似方程。在此，我们提出了针对相同可观测量的显著改进的约化阶模型，该模型适用于超越先前参数范围的情况，并通过WSINDy算法（弱形式稀疏非线性动力学识别）直接从粒子模拟中发现。该学习算法的可解释性使得能够估计先前未知的物理量，并发现具有候选物理机制的模型项，揭示了混合碰撞区域中的新物理现象。我们的方法构成了一个利用已知物理进行数据驱动模型识别的通用框架。