Emulator of PR-DNS: Accelerating Dynamical Fields With Neural Operators in Particle-Resolved Direct Numerical Simulation

Particle-resolved direct numerical simulations (PR-DNS) play an increasing role in investigating aerosol-cloud-turbulence interactions at the most fundamental level of processes. However, the high computational cost associated with high resolution simulations poses considerable challenges for large domain or long duration simulation using PR-DNS. To address these issues, here we present an emulator of the complex physics-based PR-DNS developed by use of the data-driven Fourier Neural Operator (FNO) method. The effectiveness of the method is showcased by presenting turbulence and temperature fields in a two-dimensional space. The results demonstrate high accuracy at various resolutions and the emulator is two orders of magnitude cheaper in terms of computational demand compared to the physics-based PR-DNS model. Furthermore, the FNO emulator exhibits strong generalization capabilities for different initial conditions and ultra-high-resolution without the need to retrain models. These findings highlight the potential of the FNO method as a promising tool to simulate complex fluid dynamics problems with high accuracy, computational efficiency, and generalization capabilities, enhancing our understanding of the aerosol-cloud-precipitation system. Particle-resolved direct numerical simulations (PR-DNS) are an important model to enhance our understanding of the fundamental processes involved in aerosol-cloud-turbulence interactions. However, achieving the extra-high-resolution simulations comes at very expensive computational cost. Although high-performance computing can accelerate PR-DNS simulations, it requires considering various factors, such as efficient message passing interface communications and graphics processing unit memory utilization. The machine learning (ML) emulators require much less computation cost compared to traditional numerical methods. Nevertheless, conventional ML models can only learn mappings between specific finite-dimensional spaces. The Fourier Neural Operator (FNO) method has recently been proposed to learn in the mesh-free and infinite dimensional space. In this study, we first present an emulator of the complex PR-DNS developed by using of the FNO method. The results show that the FNO model can achieve high accurate prediction, require low computational cost, and perform well with different initial conditions and resolutions, without re-training the ML models. The Fourier Neural Operator (FNO) model can accurately emulate particle-resolved direct numerical simulations (PR-DNS) at various resolutions The computational time of the physics-based PR-DNS model is reduced by two orders of magnitude with the FNO model The FNO model demonstrates robust and zero-shot generalization for various initial conditions and ultra-high resolutions