Operator Learning for Reconstructing Flow Fields from Sparse Measurements: a Language Model Approach

2026-05-22

AI Summary

Reconstructing flow fields from sparse measurements remains a fundamental challenge in fluid dynamics. This work proposes the first application of language model architectures to this task, formulating it as a sequence-to-sequence learning problem. By leveraging a mesh-free representation and a query-based mechanism, the method effectively captures spatial correlations and long-range dependencies inherent in fluid systems. Evaluated across four benchmark datasets—two-dimensional von Kármán vortex streets, daily U.S. temperature maps, three-dimensional blood flow, and turbulent jets—the approach achieves high-fidelity reconstructions even under extreme sparsity, with observation rates below 10%. The results demonstrate both computational efficiency and superior accuracy, significantly advancing the integration of scientific foundation models into flow field reconstruction.

Abstract

Reconstructing flow fields from sparse measurements is a fundamental problem in fluid mechanics with broad implications for modeling, control, and design. In this work, we propose a novel operator learning framework that leverages the architecture of language models to perform flow reconstruction in a mesh-free manner. We reformulate flow field reconstruction as a sequence-to-sequence learning task, where sparse measurements are treated as context and unobserved locations as queries. Our model learns to reconstruct the full flow field from sparse inputs, effectively capturing spatial correlations and long-range dependencies. We evaluate the proposed approach on four benchmark datasets: (1) two-dimensional vortex street simulations, (2) daily average temperature data across the contiguous United States, (3) three-dimensional blood flow simulations based on dissipative particle dynamics, and (4) three-dimensional turbulent jet flow measurements obtained via particle tracking velocimetry. Across all cases, our method demonstrates competitive reconstruction accuracy, even with highly incomplete data (less than 10\% observed), and achieves efficient performance. The results highlight the potential of language models as robust and scalable tools for scientific data reconstruction, and suggest a promising direction toward the development of foundation models for scientific and engineering applications.

Problem

• flow field reconstruction
• sparse measurements
• fluid mechanics
• operator learning
• scientific data reconstruction

Innovation

• operator learning
• language models
• flow field reconstruction
• mesh-free
• sequence-to-sequence learning