Conditional neural field latent diffusion model for generating spatiotemporal turbulence.

Eddy-resolving turbulence simulations are essential for understanding and controlling complex unsteady fluid dynamics, with significant implications for engineering and scientific applications. Traditional numerical methods, such as direct numerical simulations (DNS) and large eddy simulations (LES), provide high accuracy but face severe computational limitations, restricting their use in high-Reynolds number or real-time scenarios. Recent advances in deep learning-based surrogate models offer a promising alternative by providing efficient, data-driven approximations. However, these models often rely on deterministic frameworks, which struggle to capture the chaotic and stochastic nature of turbulence, especially under varying physical conditions and complex, irregular geometries. Here, we introduce the Conditional Neural Field Latent Diffusion (CoNFiLD) model, a generative learning framework for efficient high-fidelity stochastic generation of spatiotemporal turbulent flows in complex, three-dimensional domains. CoNFiLD synergistically integrates conditional neural field encoding with latent diffusion processes, enabling memory-efficient and robust generation of turbulence under diverse conditions. Leveraging Bayesian conditional sampling, CoNFiLD flexibly adapts to various turbulence generation scenarios without retraining. This capability supports applications such as zero-shot full-field flow reconstruction from sparse sensor data, super-resolution generation, and spatiotemporal data restoration. Extensive numerical experiments demonstrate CoNFiLD's capability to accurately generate inhomogeneous, anisotropic turbulent flows within complex domains. These findings underscore CoNFiLD's potential as a versatile, computationally efficient tool for real-time unsteady turbulence simulation, paving the way for advancements in digital twin technology for fluid dynamics. By enabling rapid, adaptive high-fidelity simulations, CoNFiLD can bridge the gap between physical and virtual systems, allowing real-time monitoring, predictive analysis, and optimization of complex fluid processes.