用能量变压器从稀疏数据重建复杂流场，90%缺失数据仍可精准还原。
Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach
- 基于关联记忆模型设计能量变压器，将不完整观测映射为完整流场。
- 在三种流体场景中实现90%数据缺失下的高精度重建，支持实验噪声数据。
- 单卡训练推理快，适用于流体力学、气象预测等领域的重建任务。
机器学习在流体力学等领域已取得显著进展，但如何从部分观测中恢复完整的速度场仍是难题。本文提出一种基于能量变压器（Energy Transformer, ET）的新颖算子学习框架，将重建问题建模为从不完整观测到完整场的映射。方法在三类流体问题上验证：(1) 圆柱绕流中的非定常二维涡街（模拟数据）；(2) 高速超声速冲击喷流（施里伦成像数据）；(3) 三维湍流喷流（粒子追踪数据）。结果表明，该方法能在高达90%数据缺失的情况下准确重构复杂流场，即使面对含噪实验测量也表现稳健，且可在单张GPU上实现快速训练与推理。本工作为流体力学及其他力学、地球物理、天气预报等领域中的重建问题提供了新思路。
原文摘要 · Abstract (English)
Machine learning methods have shown great success in various scientific areas, including fluid mechanics. However, reconstruction problems, where full velocity fields must be recovered from partial observations, remain challenging. In this paper, we propose a novel operator learning framework for solving reconstruction problems by using the Energy Transformer (ET), an architecture inspired by associative memory models. We formulate reconstruction as a mapping from incomplete observed data to full reconstructed fields. The method is validated on three fluid mechanics examples using diverse types of data: (1) unsteady 2D vortex street in flow past a cylinder using simulation data; (2) high-speed under-expanded impinging supersonic jets impingement using Schlieren imaging; and (3) 3D turbulent jet flow using particle tracking. The results demonstrate the ability of ET to accurately reconstruct complex flow fields from highly incomplete data (90\% missing), even for noisy experimental measurements, with fast training and inference on a single GPU. This work provides a promising new direction for tackling reconstruction problems in fluid mechanics and other areas in mechanics, geophysics, weather prediction, and beyond.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。