Reconstructing flow field from sparse sensor data: A deep learning framework combining autoencoder and cross-attention mechanism

Accurate reconstruction of flow fields from sparse sensor measurements remains challenging due to inherent limitations in sensor sparsity, irregular positioning, and computational inefficiency of existing methods. This study proposes a deep learning framework that integrates autoencoders with attention mechanisms through a two-stage training strategy. In the first stage, a convolutional autoencoder compresses high-resolution flow fields into low-dimensional latent representations. In the second stage, sensor data (including positions and measurements) are encoded via positional embeddings and processed by a self-attention module. These features are mapped to the latent space through a cross-attention regressor and subsequently decoded to reconstruct the complete flow field. The innovations of the proposed framework include the adaptability to arbitrary sensor numbers/positions and a significant improvement of computational efficiency. Case studies on the datasets of cylinder-wake flow and global sea surface temperature demonstrate that this framework achieves superior reconstruction accuracy, outperforming Voronoi convolutional neural network, and is comparable to the state-of-the-art Senseiver in terms of accuracy while reducing training time by 16 times. The framework also exhibits robustness against sensor failures and data noise, enabling real-time, high-precision flow reconstruction for engineering applications such as aerodynamic monitoring and climate modeling.