# Learning fast, accurate, and stable closures of a kinetic theory of an active fluid

arXiv: https://arxiv.org/abs/2308.06675 · HTML: https://mlsanity.com/paper/2308.06675/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Aug 2023.

## Built on by (most cited first, 9 of 9)

- [The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning](https://mlsanity.com/paper/2412.00568/) (2024)
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- [Overtone: Cyclic Patch Modulation for Clean, Efficient, and Flexible Physics Emulators](https://mlsanity.com/paper/2507.09264/) (2025)
- [MENO: MeanFlow-Enhanced Neural Operators for Dynamical Systems](https://mlsanity.com/paper/2604.06881/) (2026)
- [Flowers: A Warp Drive for Neural PDE Solvers](https://mlsanity.com/paper/2603.04430/) (2026)
- [Wavelet Flow Matching for Multi-Scale Physics Emulation](https://mlsanity.com/paper/2605.16573/) (2026)
- [Beyond Compression: Training Latent Representations for Stable Long-Horizon Rollout in Neural Surrogate Solvers](https://mlsanity.com/paper/2609.30198/) (2026)

## Abstract (arXiv)

Important classes of active matter systems can be modeled using kinetic theories. However, kinetic theories can be high dimensional and challenging to simulate. Reduced-order representations based on tracking only low-order moments of the kinetic model serve as an efficient alternative, but typically require closure assumptions to model unrepresented higher-order moments. In this study, we present a learning framework based on neural networks that exploit rotational symmetries in the closure terms to learn accurate closure models directly from kinetic simulations. The data-driven closures demonstrate excellent a-priori predictions comparable to the state-of-the-art Bingham closure. We provide a systematic comparison between different neural network architectures and demonstrate that nonlocal effects can be safely ignored to model the closure terms. We develop an active learning strategy that enables accurate prediction of the closure terms across the entire parameter space using a single neural network without the need for retraining. We also propose a data-efficient training procedure based on time-stepping constraints and a differentiable pseudo-spectral solver, which enables the learning of stable closures suitable for a-posteriori inference. The coarse-grained simulations equipped with data-driven closure models faithfully reproduce the mean velocity statistics, scalar order parameters, and velocity power spectra observed in simulations of the kinetic theory. Our differentiable framework also facilitates the estimation of parameters in coarse-grained descriptions conditioned on data.