A physics-informed neural operator framework is introduced 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.
Abstract
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.
Accurate modeling of collision operators is essential for reliable mesoscopic simulation of complex multiphase flows, where interfacial dynamics and long-time evolution are highly sensitive to the relaxation process. In this work, we propose a relaxation-decomposed network (RDN) for learning collision operators in discrete Boltzmann equations. The proposed model takes the discrete distribution function as the modeling variable and represents the collision term through two coupled components: an equilibrium-target correction and a relaxation-time model. These two components are parameterized by the E-net and the τ-net, respectively, leading to a structured equilibrium–relaxation formulation of the neural collision operator. Physical consistency is treated at different levels: the positivity of the constructed target equilibrium and relaxation time is enforced by the relaxation-decomposed parameterization, conservation is promoted through a soft moment-regularization term, and entropy-related behavior is assessed through theoretical estimates and numerical diagnostics. The proposed framework is instantiated within a pseudopotential lattice Boltzmann framework for multiphase flows and evaluated on representative benchmark problems, including phase separation, a static bubble, and droplet impact on a solid wall. Compared with standard neural networks and residual neural networks, numerical results show that the RDN achieves better interface preservation, smaller deviations in macroscopic quantities, and improved long-time stability during multiphase-flow evolution. The entropy-related analysis further indicates that the relaxation-decomposed structure helps maintain more stable thermodynamic behavior during long-time prediction. These results demonstrate that incorporating an explicit equilibrium–relaxation decomposition into neural collision learning provides a promising route toward robust and physically consistent mesoscopic modeling of complex multiphase flows.
Mengyu Feng, Minglei Shan, Ling Kuai et al.· The Physics of Fluids· 0 citations
Over the past decade, the Lattice Boltzmann Method (LBM) has matured into a leading framework for high-performance fluid simulation across research and industry alike. Its appeal rests on a set of properties that align unusually well with the demands of modern computing: collision and streaming operators that are strictly local, mapping naturally onto massively parallel architectures; an intrinsic ability to handle complex geometries through simple boundary rules; and a level of physical fidelity that has proven sufficient across a widening range of applications — from real-time simulation and visual effects to large-scale industrial tools such as virtual wind tunnels. The growing body of LBM-based work at SIGGRAPH and SIGGRAPH Asia reflects this trajectory directly: the method has moved from occasional appearance to recurring presence as a core computational framework. Despite this prominence, LBM has never been the subject of a dedicated SIGGRAPH course. To date, it has only been mentioned peripherally, most notably as a small component of the Real-Time Physics course at SIGGRAPH 2004. As a result, there remains a significant gap between the method’s practical importance and its formal coverage within the SIGGRAPH educational program. This lack of structured exposure has made it difficult for practitioners and researchers to fully understand the method’s foundations, strengths, limitations, and best practices for deployment on contemporary hardware. These course notes are an attempt to close that gap. Written by authors with direct experience across multiple LBM publications at SIGGRAPH over the past six years, they aim to provide something the existing literature rarely offers in a single place: a coherent path from first principles to production-oriented practice. The intent is not to survey recent work, but to equip attendees with the concepts, implementation details, and the critical perspective needed to start working with LBM solvers.
Wei Li, Chaoyang Lyu, Mengyun Liu et al.· Proceedings of the Special I...· 0 citations
The results indicate that physically meaningful molecular trajectories can emerge directly from physics-only supervision, supporting the feasibility of trajectory-unsupervised neural solvers for molecular dynamics.
Petros Triantafyllos, P. Krokidas, C. Rekatsinas· 0 citations
Conventional simulation of current-driven magnetization relies on fine-step integration of the spin-transfer-torque Landau--Lifshitz--Gilbert equation, creating a computational bottleneck in parameter sweeps and control searches. In this work, we propose a physics-constrained neural flow map that learns finite-time dynamics directly on the unit sphere. The model maps the current magnetization, spin-torque strength, and requested time span to a future state in a single forward pass. Tangent-space projection and spherical retraction preserve unit magnetization during recursive, composition-consistent rollout. We validate the framework on single-spin trajectories under in-domain torques and previously unseen but stronger drive. Beyond the training horizon, it achieves an in-domain root mean square error of $0.00425$ with norm drift at the $10^{-7}$ level. The flow outperforms an adapted Long Short-Term Memory (LSTM) in in-domain accuracy and geometric stability, although the LSTM retains slightly lower out-of-distribution state error. The resulting geometry-preserving propagator reduces reliance on fine-step integration and enables physically admissible long-horizon prediction.
Accurate and efficient simulation of edge plasma turbulence is critical for predicting confinement in fusion devices, yet Direct Numerical Simulations (DNS) remain computationally expensive. To address this bottleneck, we present a physics-informed data-driven closure scheme demonstrated on the Hasegawa-Wakatani (HW) system. Instead of using "black-box" neural networks, we leverage the Direct Interaction Approximation (DIA) to derive a rigorous closure structure with six transport coefficients, which are then identified from high-fidelity data using Physics-Informed Neural Networks (PINNs). Crucially, this approach decouples training from simulation: once the coefficients are learned, they are integrated into standard low-resolution solvers, ensuring numerical stability and physical interpretability. The resulting model (EHW-C) reproduces the spectral cascades and particle flux of high-resolution DNS with a tenfold speed-up, successfully capturing complex phenomena like inverse cascades via negative diffusion coefficients. This work serves as a proof-of-concept for developing high-fidelity, accelerated reduced-order models for more complex tokamak turbulence codes.
Kun-Peng Li, Youngwoo Cho, X. Garbet et al.· Plasma Science and Technolog...· 0 citations
This work introduces implicit machine learning force fields, which replace explicit stacks of neural network layers with self-consistent fixed-point equations, and demonstrates this across three major classes of graph neural networks: invariant, equivariant Cartesian tensor, and SO(3)-equivariant spherical-tensor architectures.
J. Maeß, Leon Werner, J. Frank et al.· arXiv.org· 0 citations
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