用生成模型提升神经算子对湍流的精细结构建模能力。
Learning Turbulent Flows with Generative Models: Super-resolution, Forecasting, and Sparse Flow Reconstruction
- 结合生成对抗训练，让神经算子保留湍流中的尖锐梯度。
- 在3D均匀各向同性湍流中，预测可达5个涡旋周转时间，提速114倍。
- 适用于实验和计算流体力学中的实时分析与控制场景。
神经算子是动力系统有前景的替代模型，但使用标准L2损失训练时往往过度平滑细尺度湍流结构。本文表明，将算子学习与生成建模结合可克服此局限。针对三种实际湍流挑战——时空超分辨率、预测与稀疏流场重建，传统神经算子均表现不佳。在施里伦喷流超分辨率任务中，对抗训练的神经算子（adv-NO）将能量谱误差降低15倍，同时保持尖锐梯度，且推理成本与普通神经算子相当。在3D均匀各向同性湍流中，adv-NO仅用单条轨迹160个时间步训练，即可准确预测长达五个涡旋周转时间，推理速度比基线扩散模型快114倍，实现近实时滚动预测。对于来自高度稀疏粒子追踪测速（PTV）类输入的圆柱尾流重建，条件生成模型能正确恢复3D速度与压力场的相位一致性和统计特性。这些进展实现了低计算开销下的高精度重建与预测，使实验与计算流体力学中的近实时分析与控制成为可能。详见项目页：https://vivekoommen.github.io/Gen4Turb/
原文摘要 · Abstract (English)
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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