Machine-Learning and Quantum Accelerated Lattice Boltzmann Methods

The Lattice Boltzmann Method (LBM) is a distribution-function-based solver for the Navier-Stokes equations, widely used in Computational Fluid Dynamics (CFD) due to its efficiency and ability to model complex flow physics (Huang et al. 2022) . However, high-resolution simulations can become computationally demanding. Leveraging the latent-state representation, quantum computing, employing superposition and entanglement, offers a potential path to overcome dimensionality constraints. As key challenge in quantum LBM (Wawrzyniak et al. 2024) remains the efficient treatment of the nonlinear, dissipative collision step. In this contribution we discuss two different approaches to bypass the classical formulation of collision operators and compare them with one another. One is based Graph Neural Networks (GNNs) that incorporates equivariances, achieving improved scalability and accuracy over previous approaches (Corbetta et al. 2023). The other is based on hybrid quantum machine learning, enabling direct incorporation into quantum LBM. We evaluate both approaches on standard benchmark cases, the Taylor-Green vortex and lid-driven cavity flow. The results indicate that both approaches can faithfully employed as surrogates for the classical collision operator formulation, and enable the efficient modeling of complex interactions.