Fast-Forward Lattice Boltzmann: Learning Kinetic Behaviour with Physics-Informed Neural Operators
This provides a faster, data-driven method for modeling kinetic systems in fluid dynamics, though it is incremental as it builds on existing neural operator approaches.
The authors tackled the computational intensity of solving the lattice Boltzmann equation by introducing a physics-informed neural operator framework that predicts flow behavior over large time horizons without step-by-step integration, demonstrating robustness in complex scenarios like vortex shedding and bubble adhesion.
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.