Learning Turbulent Flows with Generative Models: Super-resolution, Forecasting, and Sparse Flow Reconstruction

• URL: http://arxiv.org/abs/2509.08752v1
• Date: Wed, 10 Sep 2025 16:42:22 GMT
• Title: Learning Turbulent Flows with Generative Models: Super-resolution, Forecasting, and Sparse Flow Reconstruction
• Authors: Vivek Oommen, Siavash Khodakarami, Aniruddha Bora, Zhicheng Wang, George Em Karniadakis,
• Abstract summary: We show that combining operator learning with generative modeling overcomes this limitation.<n>For turbulence 3D homogeneous isotropic, adv-NO trained on only 160 timesteps from a single trajectory forecasts accurately for five eddy-turnover times.<n>For reconstructing cylinder wake flows from highly sparse Particle Tracking Velocimetry-like inputs, a conditional generative phase infers full 3D velocity and pressure fields with correct statistics.
• Score: 6.508732875368554
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural operators are promising surrogates for dynamical systems but when trained with standard L2 losses they tend to oversmooth fine-scale turbulent structures. Here, we show that combining operator learning with generative modeling overcomes this limitation. We consider three practical turbulent-flow challenges where conventional neural operators fail: spatio-temporal super-resolution, forecasting, and sparse flow reconstruction. For Schlieren jet super-resolution, an adversarially trained neural operator (adv-NO) reduces the energy-spectrum error by 15x while preserving sharp gradients at neural operator-like inference cost. For 3D homogeneous isotropic turbulence, adv-NO trained on only 160 timesteps from a single trajectory forecasts accurately for five eddy-turnover times and offers 114x wall-clock speed-up at inference than the baseline diffusion-based forecasters, enabling near-real-time rollouts. For reconstructing cylinder wake flows from highly sparse Particle Tracking Velocimetry-like inputs, a conditional generative model infers full 3D velocity and pressure fields with correct phase alignment and statistics. These advances enable accurate reconstruction and forecasting at low compute cost, bringing near-real-time analysis and control within reach in experimental and computational fluid mechanics. See our project page: https://vivekoommen.github.io/Gen4Turb/

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