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. The lattice Boltzmann method models complex flows through particle distribution functions but is limited by small time steps. The authors propose a physics-informed neural operator that advances these functions over large time steps, greatly accelerating simulations without the need to handle collisions explicitly.
Xiao Xue, Marco F. P. ten Eikelder, Mingyang Gao et al.· Nature Communications· 0 citations
On-policy self-distillation (OPSD) converts feedback into dense token-level supervision on trajectories generated by the policy to be optimized, providing a useful complement to reinforcement learning with sparse outcome rewards. However, the self-teacher policy used in OPSD is typically a stop-gradient or exponential-moving-average copy of the policy conditioned on additional context information, and thus co-evolves with both the student policy and its on-policy context distribution. Directly matching such a moving target with a fixed projection objective can lead to unstable optimization or excessive distributional concentration. This nature of OPSD motivates the proposed \emph{Self-Referenced On-Policy Self-Distillation (SR-OPSD)}. At fixed student-generated contexts, a token-level variational characterization identifies the effective distillation target as a geometric interpolation between the self-teacher policy and a reference policy. Meanwhile, we use the R\'enyi divergence family to generalize the projection geometry. This formulation separates \emph{where} the adaptive target is placed from \emph{how} the student is projected toward it: the interpolation coefficient controls underlying target, while the R\'enyi order controls the projection geometry and its sensitivity to token-level density ratios. Extensive experiments across scientific evaluation, mathematical reasoning, and coding generation tasks with multiple large language models show that SR-OPSD achieves the state-of-the-art or competitive performance across various settings.
Zhuo Sun, Entong Li, Yanlong Zhao et al.· 0 citations