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

2025-09-10

AI Summary

Traditional neural operators suffer from excessive smoothing of fine-scale turbulent structures due to L2 loss, limiting their performance in spatiotemporal super-resolution, long-term forecasting, and sparse flow-field reconstruction. To address these challenges, this work proposes adversarial neural operators (adv-NO), the first framework integrating adversarial learning, conditional generative modeling, and spectral loss into neural operators. adv-NO preserves computational efficiency while accurately capturing multiscale turbulent dynamics. Experiments demonstrate: (i) a 15× reduction in energy spectrum error for shock-containing flow super-resolution; (ii) stable 3D turbulence prediction over five vortex turnover times with 114× faster inference than high-fidelity DNS solvers; and (iii) high-fidelity reconstruction of 3D velocity and pressure fields from sparse measurements, faithfully recovering phase relationships and statistical properties.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Search and Optimization: Adversarial Search
• Multiagent Systems: Adversarial Agents

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising

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/

Problem

• Improving super-resolution of turbulent flows with generative models
• Accurately forecasting 3D turbulence dynamics with neural operators
• Reconstructing full flow fields from sparse particle tracking inputs

Innovation

• Generative adversarial training for neural operators
• Adversarially trained model reduces spectrum error
• Conditional generative model infers 3D fields