A generative diffusion framework for physically consistent 3D turbulence
Abstract
Synthesizing fully developed three-dimensional turbulence remains a long-standing problem in fluid mechanics and an open challenge for generative modeling. This difficulty arises from extreme dimensionality, multiscale fluctuations, strong intermittency, and the need to satisfy exact physical constraints, including incompressibility and prescribed mass and momentum fluxes under given boundary conditions. We propose a physics-constrained diffusion model in which some a priori constraints can be incorporated directly into the generative dynamics. Using rotating turbulence as a paradigmatic system with key geophysical applications, we assess the proposed framework. Here, we show that it enables stable and statistically faithful single-time synthesis of inertial-range three-dimensional turbulent velocity fields, accurately reproducing anisotropic energy spectra, intermittent statistics, and physical constraints, whereas standard denoising diffusion probabilistic models exhibit multiscale statistical deviations, violations of physical consistency, and substantially slower training convergence, thereby pointing to broader implications for generative modeling of high-dimensional, physically constrained complex systems.
Related
- A Self-Consistent Two-Carrier Drift-Diffusion Framework for p-n Junctions: Extended Diode Equation, Power Dissipation, and Base Transit Time
- Physically Consistent Parameter Inference: Transparent Machine Learning Emulation in High Energy Physics and Cosmology
- PINN-LPCDD: Physics-Informed Neural Network with Learnable and Physically Consistent Domain Decomposition for Compressible Multi-Medium Flows
- Physically Consistent 2D to 3D Pore Space Synthesis: 1. Dynamic Grain Packing Under Strict Morphology Constraints
- A generative foundation model for 2D magnetized plasma turbulence
BibTeX
@article{li2026generative,
title = {{A generative diffusion framework for physically consistent 3D turbulence}},
author = {Tianyi Li and Michele Buzzicotti and Fabio Bonaccorso and Luca Biferale},
journal = {Nature Communications},
year = {2026},
month = oct,
doi = {10.1038/s41467-026-78265-7},
url = {https://www.nature.com/articles/s41467-026-78265-7},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A generative diffusion framework for physically consistent 3D turbulence
AU - Tianyi Li
AU - Michele Buzzicotti
AU - Fabio Bonaccorso
AU - Luca Biferale
PY - 2026
DA - 2026/10/06
JO - Nature Communications
DO - 10.1038/s41467-026-78265-7
UR - https://www.nature.com/articles/s41467-026-78265-7
AB - Synthesizing fully developed three-dimensional turbulence remains a long-standing problem in fluid mechanics and an open challenge for generative modeling. This difficulty arises from extreme dimensionality, multiscale fluctuations, strong intermittency, and the need to satisfy exact physical constraints, including incompressibility and prescribed mass and momentum fluxes under given boundary conditions. We propose a physics-constrained diffusion model in which some a priori constraints can be incorporated directly into the generative dynamics. Using rotating turbulence as a paradigmatic system with key geophysical applications, we assess the proposed framework. Here, we show that it enables stable and statistically faithful single-time synthesis of inertial-range three-dimensional turbulent velocity fields, accurately reproducing anisotropic energy spectra, intermittent statistics, and physical constraints, whereas standard denoising diffusion probabilistic models exhibit multiscale statistical deviations, violations of physical consistency, and substantially slower training convergence, thereby pointing to broader implications for generative modeling of high-dimensional, physically constrained complex systems.
SN - 2041-1723
ER -