Fast-Forward Lattice Boltzmann: Learning Kinetic Behaviour with Physics-Informed Neural Operators

2025-09-26

AI Summary

To address the time-step restriction and high computational cost of lattice Boltzmann methods (LBM) arising from explicit collision operator evaluation, this work proposes a physics-informed neural operator framework that directly predicts the evolution of distribution functions over large time steps, bypassing conventional collision-step computation. The method incorporates momentum conservation constraints and global equivariance priors, synergistically integrating deep operator learning with kinetic system modeling to ensure physical consistency and generalizability across scales and flow regimes. Experiments demonstrate robust performance in highly nonlinear multiphase flows—including vortex shedding, liquid filament breakup, and bubble adhesion—achieving substantial speedups and enhanced spatial resolution without sacrificing fidelity. This framework establishes a new paradigm for real-time, high-fidelity LBM simulation.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Large Multimodal Models (LMMs)
• Computer Vision: Low Level & Physics-based Vision

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

The lattice Boltzmann equation (LBE), rooted in kinetic theory, provides a powerful framework for capturing complex flow behaviour by describing the evolution of single-particle distribution functions (PDFs). Despite its success, solving the LBE numerically remains computationally intensive due to strict time-step restrictions imposed by collision kernels. Here, we introduce a physics-informed neural operator framework for the LBE that enables prediction over large time horizons without step-by-step integration, effectively bypassing the need to explicitly solve the collision kernel. We incorporate intrinsic moment-matching constraints of the LBE, along with global equivariance of the full distribution field, enabling the model to capture the complex dynamics of the underlying kinetic system. Our framework is discretization-invariant, enabling models trained on coarse lattices to generalise to finer ones (kinetic super-resolution). In addition, it is agnostic to the specific form of the underlying collision model, which makes it naturally applicable across different kinetic datasets regardless of the governing dynamics. Our results demonstrate robustness across complex flow scenarios, including von Karman vortex shedding, ligament breakup, and bubble adhesion. This establishes a new data-driven pathway for modelling kinetic systems.

Problem

• Accelerating lattice Boltzmann equation solving
• Bypassing collision kernel integration steps
• Achieving discretization-invariant kinetic super-resolution

Innovation

• Physics-informed neural operators bypass collision kernel
• Discretization-invariant framework enables kinetic super-resolution
• Model-agnostic approach works across different collision dynamics