Physics-enhanced Neural Operator: An Application in Simulating Turbulent Transport

Accurate simulation of turbulent flows is of immense importance in a variety of scientific and engineering fields. 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 and thus has limited applicability to long-term and fine-scale simulation over various configurations. Given the pressing need for efficient simulation, there is an increasing interest in building machine learning models for simulating turbulence, either by reconstructing DNS from alternative low-fidelity simulations or sequentially predicting DNS from historical data. However, conventional machine learning models are not designed for capturing complex spatio-temporal characteristics of turbulent flows. This results in their limited performance and generalizability, especially when applied to complex flow data and various flow configurations. This paper presents a novel physics-enhanced neural operator (PENO) that efficiently models the complex flow dynamics while leveraging physical knowledge of partial differential equations (PDEs) to enhance the simulation process. We further introduce a self-augmentation mechanism to reduce the accumulated errors in long-term simulations. The proposed method is evaluated on multiple turbulent flow datasets, showcasing the model's capability to reconstruct high-resolution DNS data, maintain the inherent physical properties of flow transport, and transfer across various resolution settings and simulation configurations. These encouraging results confirm its applicability to a wide range of real-world scenarios in which extensive simulations are needed under diverse settings.