Physics-enhanced Neural Operator for Simulating Turbulent Transport

TL;DR

This work tackles the challenge of efficiently simulating turbulent transport with high fidelity by combining a Fourier neural operator with a PDE-aware enhancement, forming a physics-enhanced neural operator (PENO). A Runge–Kutta-based PDE branch estimates temporal gradients, and a self-augmentation scheme preserves high-frequency content to mitigate long-term error accumulation, yielding stable, accurate long-horizon predictions. Empirical results on 3D FIT and TGV datasets demonstrate that PENO, especially with self-augmentation (PENO_SA), achieves higher SSIM and lower dissipation differences than SR methods, FNO, and other baselines, while also transferring effectively to 2D vorticity flows with varying viscosity. The approach holds promise for broad, physics-consistent turbulence simulations across resolutions and PDE settings, with publicly available implementation for practical use.

Abstract

The precise simulation of turbulent flows is of immense importance in a variety of scientific and engineering fields, including climate science, freshwater science, and the development of energy-efficient manufacturing processes. Within the realm of turbulent flow simulation, direct numerical simulation (DNS) is widely considered to be the most reliable approach, but it is prohibitively expensive for long-term simulation at fine spatial scales. Given the pressing need for efficient simulation, there is an increasing interest in building machine learning models for turbulence, either by reconstructing DNS from alternative low-fidelity simulations or by predicting DNS based on the patterns learned from historical data. However, standard machine learning techniques remain limited in capturing complex spatio-temporal characteristics of turbulent flows, resulting in limited performance and generalizability. This paper presents a novel physics-enhanced neural operator (PENO) that incorporates physical knowledge of partial differential equations (PDEs) to accurately model flow dynamics. The model is further refined by a self-augmentation mechanism to reduce the accumulated error in long-term simulations. The proposed method is evaluated through its performance on two distinct sets of 3D turbulent flow data, showcasing the model's capability to reconstruct high-resolution DNS data, maintain the inherent physical properties of flow transport, and generate flow simulations across various resolutions. Additionally, experimental results on multiple 2D vorticity flow series, generated by different PDEs, highlight the transferability and generalizability of the proposed method. This confirms its applicability to a wide range of real-world scenarios in which extensive simulations are needed under diverse settings.

Figures (14)

• Figure 1: Comparison between FNO's prediction and true DNS data in the $w$ velocity channel of the forced isotropic flow. This result corresponds to a test point 0.04s (with a sampling interval of 0.002s) following the training period.
• Figure 2: The overall structure of the PENO method with self-augmentation mechanism.
• Figure 3: The recurrent unit based on Naiver Stoke equation for reconstructing turbulent flow data in the spatio-temporal field. $\textbf{Q}_{s,n}$ and $\textbf{Q}_{t,n}$ represent the spatial and temporal derivatives, respectively, at each intermediate time step.
• Figure 4: The frequency distribution from the FNO's prediction, PENO$_\text{SA}$'s prediction, and target DNS data.
• Figure 5: Change of dissipation difference by different models from 1st (5.6s) to 20th (6s) time step in the FIT dataset.