  This study introduces the Conditional Neural Field Latent Diffusion (CoNFiLD)
model, a novel generative learning framework designed for rapid simulation of
intricate spatiotemporal dynamics in chaotic and turbulent systems within
three-dimensional irregular domains. Traditional eddy-resolved numerical
simulations, despite offering detailed flow predictions, encounter significant
limitations due to their extensive computational demands, restricting their
applications in broader engineering contexts. In contrast, deep learning-based
surrogate models promise efficient, data-driven solutions. However, their
effectiveness is often compromised by a reliance on deterministic frameworks,
which fall short in accurately capturing the chaotic and stochastic nature of
turbulence. The CoNFiLD model addresses these challenges by synergistically
integrating conditional neural field encoding with latent diffusion processes,
enabling the memory-efficient and robust probabilistic generation of
spatiotemporal turbulence under varied conditions. Leveraging Bayesian
conditional sampling, the model can seamlessly adapt to a diverse range of
turbulence generation scenarios without the necessity for retraining, covering
applications from zero-shot full-field flow reconstruction using sparse sensor
measurements to super-resolution generation and spatiotemporal flow data
restoration. Comprehensive numerical experiments across a variety of
inhomogeneous, anisotropic turbulent flows with irregular geometries have been
conducted to evaluate the model's versatility and efficacy, showcasing its
transformative potential in the domain of turbulence generation and the broader
modeling of spatiotemporal dynamics.
