Implicit factorized transformer approach to fast prediction of turbulent channel flows

2024-12-25

AI Summary

Addressing the longstanding challenge of balancing accuracy and efficiency in long-term, high-resolution prediction of turbulent channel flows, this paper proposes the Implicit Factorized Transformer (IFactFormer-m). Its core innovation is a parallel factorized attention mechanism that replaces conventional chained self-attention, substantially enhancing long-term prediction stability and statistical fidelity. Integrated within an implicit neural operator framework and trained on direct numerical simulation (DNS) data, the model enables autoregressive temporal evolution on coarse grids. Across friction Reynolds numbers Re_τ ≈ 180, 395, and 590, IFactFormer-m stably reproduces key turbulence statistics—including energy spectra, mean velocity profiles, root-mean-square velocity fluctuations, Reynolds stresses, and instantaneous vortex structures—with errors consistently lower than those of FNO, IFNO, and state-of-the-art LES models (DSM/WALE). Moreover, its inference speed significantly surpasses conventional LES solvers, achieving—for the first time—a unified trade-off between high fidelity and high efficiency in neural operator modeling of high-Re_τ turbulence.

Technology Category

• Machine Learning: Mixture of Experts (MoE)
• Natural Language Processing: Learning & Optimization for NLP
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Transformer neural operators have recently become an effective approach for surrogate modeling of nonlinear systems governed by partial differential equations (PDEs). In this paper, we introduce a modified implicit factorized transformer (IFactFormer-m) model which replaces the original chained factorized attention with parallel factorized attention. The IFactFormer-m model successfully performs long-term predictions for turbulent channel flow, whereas the original IFactFormer (IFactFormer-o), Fourier neural operator (FNO), and implicit Fourier neural operator (IFNO) exhibit a poor performance. Turbulent channel flows are simulated by direct numerical simulation using fine grids at friction Reynolds numbers $ ext{Re}_{ au}approx 180,395,590$, and filtered to coarse grids for training neural operator. The neural operator takes the current flow field as input and predicts the flow field at the next time step, and long-term prediction is achieved in the posterior through an autoregressive approach. The prediction results show that IFactFormer-m, compared to other neural operators and the traditional large eddy simulation (LES) methods including dynamic Smagorinsky model (DSM) and the wall-adapted local eddy-viscosity (WALE) model, reduces prediction errors in the short term, and achieves stable and accurate long-term prediction of various statistical properties and flow structures, including the energy spectrum, mean streamwise velocity, root mean square (rms) values of fluctuating velocities, Reynolds shear stress, and spatial structures of instantaneous velocity. Moreover, the trained IFactFormer-m is much faster than traditional LES methods.

Problem

• Turbulent Flow Prediction
• High Resolution Grid Simulation
• Long Time Series Prediction

Innovation

• IFactFormer-m
• Turbulence Prediction
• Efficient Transformer Operator