PEST: Physics-Enhanced Swin Transformer for 3D Turbulence Simulation

2026-02-09

AI Summary

This work addresses the challenge that existing data-driven approaches for three-dimensional turbulence simulation struggle to simultaneously achieve long-term stability, physical consistency, and fidelity in small-scale structures, while high-fidelity direct numerical simulations remain computationally prohibitive. To overcome this, the authors propose a physics-informed 3D Swin Transformer architecture that leverages window-based self-attention to model local interactions governed by partial differential equations. The framework incorporates a frequency-domain adaptive loss to enhance the modeling of small-scale dynamics and embeds residuals of the Navier–Stokes equations along with divergence-free regularization to enforce physical consistency. Evaluated on two canonical 3D turbulent flow configurations, the method demonstrates superior long-term stability compared to current data-driven models, achieving high physical fidelity while significantly improving the reconstruction of fine-scale turbulent structures.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Web Mining and Content Analysis: Web data generation and simulation
• Search and Retrieval-Augmented AI: Large language models for search
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Accurate simulation of turbulent flows is fundamental to scientific and engineering applications. Direct numerical simulation (DNS) offers the highest fidelity but is computationally prohibitive, while existing data-driven alternatives struggle with stable long-horizon rollouts, physical consistency, and faithful simulation of small-scale structures. These challenges are particularly acute in three-dimensional (3D) settings, where the cubic growth of spatial degrees of freedom dramatically amplifies computational cost, memory demand, and the difficulty of capturing multi-scale interactions. To address these challenges, we propose a Physics-Enhanced Swin Transformer (PEST) for 3D turbulence simulation. PEST leverages a window-based self-attention mechanism to effectively model localized PDE interactions while maintaining computational efficiency. We introduce a frequency-domain adaptive loss that explicitly emphasizes small-scale structures, enabling more faithful simulation of high-frequency dynamics. To improve physical consistency, we incorporate Navier--Stokes residual constraints and divergence-free regularization directly into the learning objective. Extensive experiments on two representative turbulent flow configurations demonstrate that PEST achieves accurate, physically consistent, and stable autoregressive long-term simulations, outperforming existing data-driven baselines.

Problem

• 3D turbulence simulation
• long-horizon rollout
• physical consistency
• small-scale structures
• computational cost

Innovation

• Swin Transformer
• physics-informed learning
• 3D turbulence simulation
• frequency-domain loss
• Navier-Stokes constraints