美国科罗拉多大学Daniel A. Messenger团队揭示了物理学引导下的超冷流体力学降阶模型的弱形式发现。2025年3月17日出版的《物理评论A》杂志发表了这项成果。

课题组研究了极性分子高度碰撞、超冷但非简并气体的弛豫。气体被限制在谐波阱中，受到流体-气体耦合动力学的影响，导致一阶流体力学的崩溃。之前曾尝试使用高斯变换和粗粒度模型参数来处理这些高阶流体动力学效应，从而得出了一组可用于实验的几个集体可观测值的近似方程。

研究组为这些相同的可观测值提出了大幅改进的降阶模型，这些模型在先前的参数范围之外是可接受的，使用WSINDy算法（非线性动力学的弱形式稀疏识别）直接从粒子模拟中发现。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，从而揭示混合碰撞状态下的新物理学。该方法构成了一个利用已知物理学进行数据驱动模型识别的通用框架。

附：英文原文

Title: Physics-guided weak-form discovery of reduced-order models for trapped ultracold hydrodynamics

Author: Reuben R. W. Wang, Daniel A. Messenger

Issue&Volume: 2025/03/17

Abstract: 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 and 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.

DOI: 10.1103/PhysRevA.111.033311

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.111.033311