CoNFiLD: Conditional Neural Field Latent Diffusion Model Generating Spatiotemporal Turbulence*

This study presents the Conditional Neural Field Latent Diffusion (CoNFiLD) model, a novel generative AI method for rapid simulation of spatiotemporal chaotic/turbulent dynamics within three-dimensional irregular domains. Traditional eddy-resolved numerical simulations, despite offering detailed flow predictions, are limited by their extensive computational demands, restricting their broader engineering applications. In contrast, deep learning-based surrogate models promise efficient, data-driven solutions but often fall short in capturing the chaotic and stochastic nature of turbulence due to their reliance on deterministic frameworks. The CoNFiLD model addresses these challenges by integrating conditional neural field encoding with latent diffusion processes, enabling memory-efficient and robust probabilistic generation of spatiotemporal turbulence under varied conditions. Using Bayesian conditional sampling, the model adapts to diverse turbulence generation scenarios without retraining, covering zero-shot full-field flow reconstruction from sparse sensor measurements to super-resolution generation and spatiotemporal flow data restoration. Comprehensive numerical experiments on various inhomogeneous, anisotropic turbulent flows with irregular geometries have been conducted to evaluate the model's versatility and efficacy, showcasing its transformative potential in turbulence generation and broader spatiotemporal dynamics modeling.