ViTAE-SL: A vision transformer-based autoencoder and spatial interpolation learner for field reconstruction

Abstract

Reliable and accurate reconstruction for large-scale and complex physical fields in real-time from limited observations has been a longstanding challenge. In recent years, sensors have been increasingly deployed in numerous physical systems. However, the locations of these sensors can shift over time, such as with mobile sensors, or when sensors are deployed and removed. These sparse and randomly located sensors further exacerbate the difficulty of reconstructing the physical field. In this paper, we present a new deep learning model called Vision Transformer-based Autoencoder (ViTAE) for reconstructing large-scale and complex fields. The proposed network structure is based on a novel core design: vision transformer encoder and Convolutional Neural Network (CNN) decoder. First, we split a two-dimensional field into patches and developed a vision transformer encoder to transfer patches into latent representations. We then reshape the linear latent representations to patches before concatenation, along with a CNN decoder, to reconstruct the field. The proposed model is tested in four different numerical experiments, using generated synthetic data, spatially distributed PM2.5 data, Computational Fluid Dynamics (CFD) simulation data and National Oceanic and Atmospheric Administration (NOAA) sea surface temperature data. The numerical results highlight the strength of ViTAE-SL compared to Kriging and state-of-the-art deep-learning models with significantly higher reconstruction accuracy, computational efficiency, and robust scaling behavior.