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

arXiv: https://arxiv.org/abs/2406.07519 · HTML: https://mlsanity.com/paper/2406.07519/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 25 references that are in the map.
- First posted on arXiv 11 Jun 2024.

## Builds on (most cited first, 5 of 5)

- [Weak SINDy For Partial Differential Equations](https://mlsanity.com/paper/2007.02848/) (2020)
- [Deep learning of thermodynamics-aware reduced-order models from data](https://mlsanity.com/paper/2007.03758/) (2020)
- [Learning Mean-Field Equations from Particle Data Using WSINDy](https://mlsanity.com/paper/2110.07756/) (2021)
- [Learning Discrepancy Models From Experimental Data](https://mlsanity.com/paper/1909.08574/) (2019)
- [Coarse-Graining Hamiltonian Systems Using WSINDy](https://mlsanity.com/paper/2310.05879/) (2023)

## Built on by (most cited first, 2 of 2)

- [Learning effective models from network dynamics data with multiple initial conditions using weak form SINDy](https://mlsanity.com/paper/2605.30432/) (2026)
- [Tensor-Train Weak SINDy: Identifying High-Dimensional Nonlinear Dynamics](https://mlsanity.com/paper/2609.09434/) (2026)

## Abstract (arXiv)

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.