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

TL;DR

This work addresses the challenge of efficiently modeling high-dimensional CFD outputs by learning a discrete latent space with a VQ-VAE and comparing quantum (QCBM, QGAN) and classical (LSTM) generative models for sampling from this latent prior. It presents an end-to-end, open-source pipeline that couples a GPU-accelerated LBM for data generation with latent-space learning and subsequent quantum/classical sampling, evaluated through both visualization and quantitative metrics. The key finding is that quantum models, particularly QCBM with per-dimension independence, can produce samples closer to the true latent distribution than the LSTM baseline under the tested conditions, suggesting potential advantages of quantum approaches in physics-informed latent modeling. This exploratory study lays the groundwork for rigorous benchmarking, physical validation, and eventual deployment on larger CFD problems and real quantum hardware, highlighting directions for future research in quantum-assisted CFD data generation and augmentation.

Abstract

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.

Figures (13)

• Figure 1: Snapshot from the LBM-generated dataset showing vorticity field for flow around a cylinder at Re=500.
• Figure 2: VQ-VAE architecture showing encoder, quantization module with codebook, and decoder.
• Figure 3: Distribution of continuous latent space values, showing approximately Gaussian characteristics.
• Figure 4:
• Figure 5: QCBM learned distributions (blue) compared to target distributions (green) for latent dimensions 1 and 7.