Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach

TL;DR

This paper introduces an Energy Transformer-based operator learning framework that accurately reconstructs complex fluid flow fields from highly incomplete and noisy data, demonstrating its effectiveness across multiple fluid mechanics scenarios.

Contribution

The paper presents a novel Energy Transformer architecture for operator learning, specifically designed for reconstructing flow fields from sparse measurements, advancing the capabilities in fluid mechanics data assimilation.

Findings

Accurately reconstructs flow fields from 90% missing data.

Performs well with noisy experimental measurements.

Achieves fast training and inference on a single GPU.

Abstract

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.