Deep learning with Fourier Neural Operators for sedimentary structure recognition

Sedimentary structure classification is fundamental to facies interpretation, depositional environment reconstruction, and reservoir characterization. While Convolutional Neural Networks (CNNs) have demonstrated success in geological image analysis, their spatial-domain operations may limit their ability to capture repetitive and globally organized stratification patterns. In this study, we introduce a Fourier Neural Operator (FNO)-based framework for automated classification of eleven sedimentary structure classes from core images and benchmark it against EfficientNet-B2, ResNet-50, MobileNet-V3, and a transformer-based Vision Transformer (ViT), specifically the Data-efficient Image Transformer (DeiT-B16), under a harmonized 5-fold cross-validation protocol. The FNO achieved the highest overall accuracy (0.986) and macro-averaged F1-score (0.983), outperforming EfficientNet-B2 (0.975), DeiT-B16 (0.972), MobileNet-V3 (0.967), and ResNet-50 (0.960). Paired statistical tests across folds confirmed that performance differences between FNO and all benchmark models are statistically significant (p < 0.05). Precision-recall curves further demonstrate balanced class-wise performance despite dataset imbalance, with average precision (AP) values exceeding 0.98 across all classes. Ablation analysis revealed that performance gains are attributable to learned frequency-domain representations rather than increased model capacity. Removal of Fourier blocks leads to systematic degradation and confusion patterns. Additional frequency-domain visualizations provided an intuitive illustration of how representative bedding geometries are preserved in the retained low-frequency content and refined through the spectral layers of the FNO. An additional resolution-robustness analysis showed that FNO retained the highest prediction stability under progressive image degradation, indicating stronger tolerance to reduced image detail than the benchmark models. Despite containing substantially fewer parameters (0.01 M) and lower computational cost (0.21 GFLOPs), FNO achieved both the highest predictive accuracy and the lowest inference latency (0.0023 s per image). These results indicate that frequency-domain modeling provides measurable and statistically supported improvements for sedimentary structure classification, particularly for rhythmically layered structure facies.