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

TL;DR

This work tackles the challenge of denoising DAS data when training labels are imperfect due to residual coupling noise. It introduces PAUFNO, a physics-aware, U-Net–enhanced Fourier Neural Operator that learns mappings between function spaces, augmented by a dual-triangle FK-domain loss and a patch-based training workflow. The approach demonstrates superior denoising performance on Utah FORGE DAS data and shows robust generalization to unseen Groß Schönebeck data, with Monte Carlo Dropout enabling uncertainty quantification. The method offers a practical, physics-informed pathway to improve DAS signal recovery and could extend to wavefield separation and other transform-domain denoising tasks.

Abstract

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.

Figures (13)

• Figure 1: Diagram of the proposed DAS denoising framework. The model begins with an uplifting layer ($P$) that projects the input features into a higher-dimensional space. The resulting feature maps are then processed in parallel by the UFNO and FNO blocks, followed by an efficient channel attention (ECA) module that captures fine-grained information in both the spatial and frequency domains. Unlike the standard FNO block, the UFNO branch includes an additional U-Net channel to enhance feature representation in the time domain. Finally, a projection layer ($Q$) maps the high-dimensional features back to the input dimensionality to produce the denoised output. The symbol $\sigma$ denotes the activation function.
• Figure 2: Inference workflow of the trained operator. The input noisy records are first divided into overlapping patches with fixed dimensions. These noisy patches are then processed by the trained operator to perform denoising. After obtaining the denoised patches, an inverse patching scheme is applied to reconstruct the full denoised output. It is worth noting that the trained operator can effectively handle patches with resolutions different from those used during training, as it learns underlying functional relationships rather than fixed nonlinear mappings within finite domains.
• Figure 3: Diagram of the physics-aware loss function. (a) Dual-triangle masking setup, where the green dot indicates the zero wavenumber point, as well as the zero point of the normalized frequency. (b) Warmup factor of the physics-aware loss, where the factor rises from 0 to 1 to avoid useful signal damages in the early training stage.
• Figure 4: Denoising comparisons of different methods on DAS record with multiple events. (a) is the raw data. (b–e) are corresponding to denoised records using BPSOMFFK, PAUFNO, UFNO, and U-Net, respectively. (f–i) display removed noise with BPSOMFFK, Proposed, UFNO, and U-Net, respectively.
• Figure 5: Zoomed-in comparisons of denoising results from Figure \ref{['fig:eq_36_seis']}. The first row shows the raw data and denoising profiles using different methods. The yellow rectangles in the second row indicate regions affected by residual clipping noise, which are enlarged in the second row. The green rectangles highlight areas containing both coupling noise and signal, shown in the third row. The bottom row presents zoomed-in sections corresponding to regions dominated by signals only.