Generative AI for fast and accurate Statistical Computation of Fluids

2024-09-27

arXiv.org

AI Summary

High-fidelity, computationally efficient statistical modeling of three-dimensional turbulent flows remains challenging for conventional deterministic machine learning methods, which often suffer from mean regression artifacts. Method: This paper proposes GenCFD, an end-to-end conditional score-based diffusion model for turbulence generation. Unlike standard regression approaches, GenCFD theoretically elucidates the intrinsic mechanism by which diffusion models synthesize turbulent fields, and integrates spectral-resolution-aware architecture design, joint modeling of key turbulence statistics (e.g., energy spectra, structure functions), and physics-informed generative principles. Results: Evaluated across multiple challenging turbulent flow configurations, GenCFD simultaneously achieves superior statistical fidelity and sample realism—outperforming MSE-based regression baselines with significantly reduced spectral error. The framework advances both statistical accuracy and physical plausibility in data-driven turbulence modeling. Open-source implementation is provided.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Natural Language Processing: Generation
• Computer Vision: Diffusion Models for Vision

Application Category

• Web Mining and Content Analysis: Web data generation and simulation
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

We present a generative AI algorithm for addressing the pressing task of fast, accurate, and robust statistical computation of three-dimensional turbulent fluid flows. Our algorithm, termed as GenCFD, is based on an end-to-end conditional score-based diffusion model. Through extensive numerical experimentation with a set of challenging fluid flows, we demonstrate that GenCFD provides an accurate approximation of relevant statistical quantities of interest while also efficiently generating high-quality realistic samples of turbulent fluid flows and ensuring excellent spectral resolution. In contrast, ensembles of deterministic ML algorithms, trained to minimize mean square errors, regress to the mean flow. We present rigorous theoretical results uncovering the surprising mechanisms through which diffusion models accurately generate fluid flows. These mechanisms are illustrated with solvable toy models that exhibit the mathematically relevant features of turbulent fluid flows while being amenable to explicit analytical formulae. Our codes are publicly available at https://github.com/camlab-ethz/GenCFD.

Problem

• 三维乱流
• 智能算法
• 计算效率

Innovation

• GenCFD
• 3D Turbulent Flow Simulation
• High-Definition Visualization