<p>Accurate porosity prediction from well logs is critical for reservoir characterization, yet existing deep learning approaches face notable limitations. Sequential LSTM-based architectures suffer from computational bottlenecks due to their recurrent processing of depth sequences, which limits training efficiency and scalability on large well-log datasets. Single-pass CNN-Transformer models, while more parallelizable, often fail to preserve multi-scale features, resulting in inadequate capture of geological heterogeneity across varying stratigraphic resolutions. To address these challenges, we propose a novel 1D U-Net architecture that integrates ResNet blocks with dual attention mechanisms and is trained using Huber loss for robust handling of well-log noise. The encoder-decoder structure employs residual blocks for efficient, parallelized processing of depth-windowed sequences, overcoming LSTM’s sequential bottlenecks while preserving multi-resolution features through skip connections enhanced by attention gates. Self-attention at the bottleneck further captures global stratigraphic patterns across depth intervals, compensating for the limited multi-scale representation in standard CNN-Transformer designs. Huber loss (with δ = 0.005 calibrated to the empirical distribution of training residuals) combines quadratic penalties for high-precision fitting in tight formations and linear penalties for outlier robustness, with approximately 24.7% of residuals engaging the linear regime to mitigate measurement artifacts common in well-log data. We evaluate the model on a carbonate reservoir dataset using blind well testing. Compared to baselines including CNN-Transformer, PPTransformer, U-Net-LSTM, and PSO-GBDT, our architecture achieves superior performance with R² = 0.9912 ± 0.0008 and RMSE = 0.0042 ± 0.0003, while training approximately 7 times faster than U-Net-LSTM. Autocorrelation-corrected paired t-tests with empirically justified effective sample size (<InlineEquation ID="IEq1"><EquationSource Format="TEX">\(\:{N}_{eff}\approx\:200\)</EquationSource></InlineEquation>, <InlineEquation ID="IEq2"><EquationSource Format="TEX">\(\:lag-1\:\rho\:\approx\:0.98\)</EquationSource></InlineEquation>) and large effect sizes (Cohen’s d > 0.8) confirm statistically significant improvements at <InlineEquation ID="IEq3"><EquationSource Format="TEX">\(\:\alpha\:=0.05\)</EquationSource></InlineEquation> across all baseline comparisons. Attention visualizations demonstrate focus on lithologically sensitive depth intervals, enhancing geological interpretability. This work establishes ResNet-based encoder-decoder architectures with dual attention and robust loss functions as an efficient and accurate framework for well log-based porosity prediction.</p>

Dual-attention residual U-Net with Huber loss for robust and efficient porosity prediction from well logs

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2026年5月28日

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Amirreza Mehrabi,
Matin Mahzad,
Majid Bagheri,
Majid Nabi Bidhendi

摘要

Accurate porosity prediction from well logs is critical for reservoir characterization, yet existing deep learning approaches face notable limitations. Sequential LSTM-based architectures suffer from computational bottlenecks due to their recurrent processing of depth sequences, which limits training efficiency and scalability on large well-log datasets. Single-pass CNN-Transformer models, while more parallelizable, often fail to preserve multi-scale features, resulting in inadequate capture of geological heterogeneity across varying stratigraphic resolutions. To address these challenges, we propose a novel 1D U-Net architecture that integrates ResNet blocks with dual attention mechanisms and is trained using Huber loss for robust handling of well-log noise. The encoder-decoder structure employs residual blocks for efficient, parallelized processing of depth-windowed sequences, overcoming LSTM’s sequential bottlenecks while preserving multi-resolution features through skip connections enhanced by attention gates. Self-attention at the bottleneck further captures global stratigraphic patterns across depth intervals, compensating for the limited multi-scale representation in standard CNN-Transformer designs. Huber loss (with δ = 0.005 calibrated to the empirical distribution of training residuals) combines quadratic penalties for high-precision fitting in tight formations and linear penalties for outlier robustness, with approximately 24.7% of residuals engaging the linear regime to mitigate measurement artifacts common in well-log data. We evaluate the model on a carbonate reservoir dataset using blind well testing. Compared to baselines including CNN-Transformer, PPTransformer, U-Net-LSTM, and PSO-GBDT, our architecture achieves superior performance with R² = 0.9912 ± 0.0008 and RMSE = 0.0042 ± 0.0003, while training approximately 7 times faster than U-Net-LSTM. Autocorrelation-corrected paired t-tests with empirically justified effective sample size (\(\:{N}_{eff}\approx\:200\), \(\:lag-1\:\rho\:\approx\:0.98\)) and large effect sizes (Cohen’s d > 0.8) confirm statistically significant improvements at \(\:\alpha\:=0.05\) across all baseline comparisons. Attention visualizations demonstrate focus on lithologically sensitive depth intervals, enhancing geological interpretability. This work establishes ResNet-based encoder-decoder architectures with dual attention and robust loss functions as an efficient and accurate framework for well log-based porosity prediction.