# Quantum Generative Models for Computational Fluid Dynamics: A First Exploration of Latent Space Learning in Lattice Boltzmann Simulations

arXiv: https://arxiv.org/abs/2512.22672 · HTML: https://mlsanity.com/paper/2512.22672/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 32 references that are in the map.
- First posted on arXiv 27 Dec 2025.

## Builds on (most cited first, 8 of 8)

- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [Professor Forcing: A New Algorithm for Training Recurrent Networks](https://mlsanity.com/paper/1610.09038/) (2016)
- [Quantum generative adversarial networks](https://mlsanity.com/paper/1804.08641/) (2018)
- [A Framework for Demonstrating Practical Quantum Advantage: Racing Quantum against Classical Generative Models](https://mlsanity.com/paper/2303.15626/) (2023)
- [Quantum-Informed Machine Learning for Predicting Spatiotemporal Chaos with Practical Quantum Advantage](https://mlsanity.com/paper/2507.19861/) (2025)

## Abstract (arXiv)

This paper presents the first application of quantum generative models to learned latent space representations of computational fluid dynamics (CFD) data. While recent work has explored quantum models for learning statistical properties of fluid systems, the combination of discrete latent space compression with quantum generative sampling for CFD remains unexplored. We develop a GPU-accelerated Lattice Boltzmann Method (LBM) simulator to generate fluid vorticity fields, which are compressed into a discrete 7-dimensional latent space using a Vector Quantized Variational Autoencoder (VQ-VAE). The central contribution is a comparative analysis of quantum and classical generative approaches for modeling this physics-derived latent distribution: we evaluate a Quantum Circuit Born Machine (QCBM) and Quantum Generative Adversarial Network (QGAN) against a classical Long Short-Term Memory (LSTM) baseline. Under our experimental conditions, both quantum models produced samples with lower average minimum distances to the true distribution compared to the LSTM, with the QCBM achieving the most favorable metrics. This work provides: (1)~a complete open-source pipeline bridging CFD simulation and quantum machine learning, (2)~the first empirical study of quantum generative modeling on compressed latent representations of physics simulations, and (3)~a foundation for future rigorous investigation at this intersection.