Fast-forward prediction of lattice Boltzmann dynamics with physics-informed neural operators

The lattice Boltzmann equation (LBE), rooted in kinetic theory, captures complex flow behaviour by evolving single-particle distribution functions (PDFs), but its explicit time-stepping makes large-scale simulation computationally intensive. Here we introduce a physics-informed neural operator framework that predicts the LBE evolution over large time jumps without performing step-by-step forward integration, bypassing the need to solve the collision kernel explicitly. The model embeds intrinsic moment-matching constraints and global equivariance of the distribution field, preserving the kinetic structure of the underlying system. The framework is discretization-invariant: models trained on coarse-grained PDFs perform inference on finer grids even when the relaxation time differs between resolutions. It is also agnostic to the lattice Boltzmann formulation, allowing the same architecture to be reused across different kinetic datasets. Across von Kármán vortex shedding, ligament breakup, and bubble adhesion, the framework offers a robust data-driven pathway for accelerating the lattice Boltzmann based dynamical systems.