High-speed turbulent flows interacting with deformable surfaces pose challenges for data collection, leading to sparse, undersampled pressure signals. In this study, we develop a Transformer-based deep learning model to reconstruct missing pressure data in a shock/boundary-layer interaction over a flexible panel. Starting from sparsely sampled pressure time series, we apply cubic spline interpolation to produce a continuous initial estimate, which the Transformer then maps to the actual pressure signal. We evaluate the model at multiple sensor locations across various levels of data sparsity (ranging from 50% to 6% of the original samples) and compare its performance with the interpolation baseline. Our results show that at moderate sparsity (50% data points), the Transformer and spline interpolation attain similar accuracy, but as sparsity increases, the Transformer consistently outperforms the spline. At the highest sparsity tested, the Transformer's mean squared error is over 20% lower than that of spline interpolation. The Transformer's predictions closely match the true signals across most of the time and frequency content, successfully preserving turbulent pressure fluctuations that cubic spline interpolation fails to capture at high frequencies. These findings demonstrate the robustness of Transformer architectures for reconstructing complex fluid-dynamic sensor data from limited observations. The proposed method enables more precise recovery of pressure signals in high-speed flow applications, highlighting a promising direction for integrating physics-based interpolation with deep learning in fluid dynamics. Future research directions to improve the models at high frequencies are also proposed.
Drikakis et al. (Sun,) studied this question.