# Spatial-Frequency-Scale Variational Autoencoder for Enhanced Flow Diagnostics of Schlieren Data

## TL;DR

A new deep learning model called SFS-VAE improves the analysis of Schlieren data for better flow diagnostics and predictions.

## Contribution

The novel SFS-VAE framework introduces modules for multi-scale and frequency-based feature extraction in Schlieren data analysis.

## Key findings

- SFS-VAE reduces RMSE by 16.9% and increases PSNR by 1.6 dB in Schlieren data analysis.
- The model improves temporal prediction stability and accuracy when combined with a Transformer.
- It effectively captures high-gradient jet region features while preserving mainstream information.

## Abstract

Schlieren imaging is a powerful optical sensing technique that captures flow-induced refractive index gradients, offering valuable visual data for analyzing complex fluid dynamics. However, the large volume and structural complexity of the data generated by this sensor pose significant challenges for extracting key physical insights and performing efficient reconstruction and temporal prediction. In this study, we propose a Spatial-Frequency-Scale variational autoencoder (SFS-VAE), a deep learning framework designed for the unsupervised feature decomposition of Schlieren sensor data. To address the limitations of traditional β-variational autoencoder (β-VAE) in capturing complex flow regions, the Progressive Frequency-enhanced Spatial Multi-scale Module (PFSM) is designed, which enhances the structures of different frequency bands through Fourier transform and multi-scale convolution; the Feature-Spatial Enhancement Module (FSEM) employs a gradient-driven spatial attention mechanism to extract key regional features. Experiments on flat plate film-cooled jet schlieren data show that SFS-VAE can effectively preserve the information of the mainstream region and more accurately capture the high-gradient features of the jet region, reducing the Root Mean Square Error (RMSE) by approximately 16.9% and increasing the Peak Signal-to-Noise Ratio (PSNR) by approximately 1.6 dB. Furthermore, when integrated with a Transformer for temporal prediction, the model exhibits significantly improved stability and accuracy in forecasting flow field evolution. Overall, the model’s physical interpretability and generalization ability make it a powerful new tool for advanced flow diagnostics through the robust analysis of Schlieren sensor data.