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

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arxiv 2409.08477 v2 pith:SYHLGX3I submitted 2024-09-13 cs.LG cs.AIphysics.flu-dyn

Vivek Oommen , Aniruddha Bora , Zhen Zhang , George Em Karniadakis This is my paper · ORCID
classification cs.LGcs.AIphysics.flu-dyn
keywords neuraloperatorsmodelsdiffusionmodelingspectralturbulentflow
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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

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