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

2024-09-13

arXiv.org

AI Summary

Neural operators often inadequately capture high-frequency turbulent dynamics, leading to distorted energy spectra and excessive smoothing. To address this, we propose a neural operator–diffusion model synergy: for the first time, conditional diffusion models leverage coarse-grained priors generated by Fourier- or graph-based neural operators to drive high-fidelity turbulent structure reconstruction. Our method integrates diffusion-based correction into autoregressive rollout and imposes POD spectral constraints, trained on Schlieren velocimetry experimental data. The key contribution is a novel coupling framework that bridges generative modeling with physics-informed operators, significantly enhancing spatiotemporal spectral fidelity and long-term forecast stability. Experiments demonstrate superior vortex-resolving accuracy on high-Reynolds-number jets and real experimental data, with predicted energy spectra showing markedly improved agreement with ground-truth distributions.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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

Problem

• Enhances turbulent flow spectral representation.
• Overcomes neural operators' high-frequency deficiencies.
• Combines diffusion models with neural operators.

Innovation

• Neural operators enhance computational efficiency
• Diffusion models correct high-frequency dynamics
• Combined approach improves spectral fidelity