Deep learning with fourier features for regressive flow field reconstruction from sparse sensor measurements.

Area of Science:

• Computational fluid dynamics
• Fluid mechanics
• Deep learning applications

Background:

• Reconstructing flow fields from limited sensor data is crucial but challenging due to ill-conditioned measurement operators.
• Existing data-driven methods often lack generalizability across different flow conditions and suffer from spectral bias, leading to inaccurate reconstructions.

Purpose of the Study:

• To introduce FLRNet, a novel deep learning approach for accurate flow field reconstruction from sparse sensor measurements.
• To address the limitations of current methods, including poor generalizability and spectral bias.

Main Methods:

• FLRNet utilizes a variational autoencoder with Fourier feature layers to learn a low-dimensional latent representation of the flow field.
• An attention-based network correlates the latent representation with sensor measurements, incorporating a perceptual loss term for improved training.

Main Results:

• FLRNet demonstrated superior reconstruction accuracy and generalizability across diverse fluid flow conditions and sensor configurations.
• The method consistently outperformed baseline approaches in all tested scenarios, showing high robustness to noise.

Conclusions:

• FLRNet offers an effective solution for flow field reconstruction from sparse data, overcoming limitations of existing techniques.
• The deep learning approach shows significant promise for applications in computational and experimental fluid mechanics.