Learning from Imperfect Labels: A Physics-Aware Neural Operator with Application to DAS Data Denoising

Supervised deep learning methods typically require large datasets and high-quality labels to achieve reliable predictions. However, their performance often degrades when trained on imperfect labels. To address this challenge, we propose a physics-aware loss function that serves as a penalty term to mitigate label imperfections during training. In addition, we introduce a modified U-Net-Enhanced Fourier Neural Operator (UFNO) that achieves high-fidelity feature representation while leveraging the advantages of operator learning in function space. By combining these two components, we develop a physics-aware UFNO (PAUFNO) framework that effectively learns from imperfect labels. To evaluate the proposed framework, we apply it to the denoising of distributed acoustic sensing (DAS) data from the Utah FORGE site. The label data were generated using an integrated filtering-based method, but still contain residual coupling noise in the near-wellbore channels. The denoising workflow incorporates a patching-based data augmentation strategy, including an uplifting step, spatial-domain convolutional operations, spectral convolution, and a projection layer to restore data to the desired shape. Extensive numerical experiments demonstrate that the proposed framework achieves superior denoising performance, effectively enhancing DAS records and recovering hidden signals with high accuracy.