Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modeling

2024/09/13 by Vivek Oommen, Oommen, Vivek, Aniruddha Bora +5 · 8 citations
Engineering · Physics and Astronomy · #Artificial Intelligence (cs.AI) #Energy Load and Power Forecasting #FOS: Computer and information sciences #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Machine Learning (cs.LG) #Model Reduction and Neural Networks

paper · pdf · doi:10.48550/arxiv.2409.08477

openalex publication_date 2024/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We integrate neural operators with diffusion models to address the spectral limitations of neural operators in surrogate modeling of turbulent flows. While neural operators offer computational efficiency, they exhibit deficiencies in capturing high-frequency flow dynamics, resulting in overly smooth approximations. To overcome this, we condition diffusion models on neural operators to enhance the resolution of turbulent structures. Our approach is validated for different neural operators on diverse datasets, including a high Reynolds number jet flow simulation and experimental Schlieren velocimetry. The proposed method significantly improves the alignment of predicted energy spectra with true distributions compared to neural operators alone. This enables the diffusion models to stabilize longer forecasts through diffusion-corrected autoregressive rollouts, as we demonstrate in this work. Additionally, proper orthogonal decomposition analysis demonstrates enhanced spectral fidelity in space-time. This work establishes a new paradigm for combining generative models with neural operators to advance surrogate modeling of turbulent systems, and it can be used in other scientific applications that involve microstructure and high-frequency content. See our project page: vivekoommen.github.io/NO_DM

Cited by

• Autoregressive One-Step Generative Modeling for Dynamical System Forecasting
• Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations
• Reconstructing Multi-Scale Physical Fields from Extremely Sparse Measurements with an Autoencoder-Diffusion Cascade
• Importance of localized dilatation and distensibility in identifying determinants of thoracic aortic aneurysm with neural operators
• Reframing Generative Models for Physical Systems using Stochastic Interpolants
• Flow marching for a generative PDE foundation model
• A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learning
• DETNO: A Diffusion-Enhanced Transformer Neural Operator for Long-Term Traffic Forecasting

Related

• Mitigating Spectral Bias in Neural Operators via High-Frequency Scaling for Physical Systems
• Towards Long-Term predictions of Turbulence using Neural Operators
• Learning Turbulent Flows with Generative Models: Super-resolution, Forecasting, and Sparse Flow Reconstruction
• Fourier neural operators for spatiotemporal dynamics in two-dimensional turbulence
• Neural Differentiable Modeling with Diffusion-Based Super-resolution for Two-Dimensional Spatiotemporal Turbulence