GeoGraphFormer: A Direction-Aware Graph Transformer for Regional Polymetallic Mineral Prospectivity Mapping

Technical Summary: GeoGraphFormer for Regional Polymetallic Mineral Prospectivity Mapping

Problem Statement
Regional Mineral Prospectivity Mapping (MPM) faces significant challenges in accurately representing structurally controlled mineralization. Traditional statistical and machine learning methods often treat spatial evidence as isotropic, failing to capture the directional continuity of ore-forming processes along faults, intrusive contacts, and stratigraphic boundaries. While Graph Neural Networks (GNNs) like Graph Convolutional Networks (GCNs) and Graph Attention Networks (GATs) have improved upon raster-based methods by modeling spatial topology, they suffer from critical limitations: GCNs aggregate features isotropically, averaging out directional signals, while GATs focus on feature content without explicitly encoding the orientation of spatial relationships. Furthermore, standard Graph Transformers, while capable of capturing long-range dependencies, typically treat pairwise spatial relationships symmetrically, lacking the mechanism to distinguish orientation-dependent geological interactions essential for modeling anisotropic geochemical gradients and structural controls.

Methodology
To address these limitations, the authors propose GeoGraphFormer, a direction-aware Graph Transformer framework designed for regional polymetallic mineral prospectivity mapping in the Lhasa-Woka metallogenic belt. The methodology integrates geological domain knowledge into the deep learning architecture through the following components:

1. Data Preprocessing and Feature Engineering:

   • Input Data: The model utilizes a 43-band geochemical-structural dataset comprising 39 elemental concentration rasters, one fracture-density layer, and three isometric log-ratio (ILR) balance variables (B7, B8, B9).
   • Compositional Data Analysis (CoDA): To address the closure problem in geochemical data, the 39 elemental variables are transformed into three ILR balances using a Sequential Binary Partition (SBP) method. These balances represent specific mineralization associations (e.g., ore-forming/pathfinder elements, Cu-Mo vs. W-Sn differentiation, and Pb-Zn associations).
   • Tokenization: The study area is partitioned into 16×16 pixel tiles (125m resolution). Each tile is tokenized into 16 non-overlapping 4×4 patches, creating a sequence of spatial tokens with a 43-dimensional feature vector per patch.

2. Model Architecture:

   • GeoBandWeighting: A learnable gating mechanism applied before patch embedding that adaptively weights the 43 input channels, allowing the model to suppress uninformative spectral bands and amplify geochemically relevant ones.
   • Patch Embedding & Positional Encoding: Patches are projected into a hidden dimension (128) and augmented with 2D sinusoidal positional encodings to preserve absolute spatial location.
   • GeoRelAttn (Directional Relational Attention): The core innovation replaces standard self-attention with a mechanism that incorporates learnable directional biases. The attention score between any two patches is modulated by a learnable scalar bias corresponding to one of nine spatial relations: North, South, East, West, Northeast, Northwest, Southeast, Southwest, and Self. This allows the model to learn orientation-dependent attention patterns rather than treating all neighbors equally.
   • GeoBlocks & Classification: The architecture stacks three GeoBlocks (each containing GeoRelAttn and a Feed-Forward Network) followed by a CLS token-based classification head for binary prediction (mineralized vs. non-mineralized).

3. Training and Evaluation Strategy:

   • Ensemble Learning: To mitigate overfitting given the limited labeled dataset (234 tiles: 117 mineralized, 117 non-mineralized), the authors trained an ensemble of 10 models with different random seeds. The final prediction is derived from a greedy selection of the top 5 models based on validation AUC.
   • Regularization: Techniques include label smoothing (ε=0.05), Exponential Moving Average (EMA) of parameters, Monte Carlo Dropout for uncertainty estimation, and data augmentation (flips and rotations).
   • Metrics: Performance is evaluated using Accuracy, ROC-AUC, PR-AUC, F1-score, Sensitivity, and Specificity on a held-out test set.

Key Results
Evaluated on the Lhasa-Woka test set, GeoGraphFormer achieved:

• Accuracy: 91.67%
• ROC-AUC: 0.9444
• PR-AUC: 0.9478
• F1-Score: 0.9167
• Sensitivity/Specificity: Both 91.67%

The model significantly outperformed baseline GCN (81.25% accuracy, 0.8681 AUC) and GAT (83.33% accuracy, 0.8854 AUC) models. Notably, GeoGraphFormer maintained balanced sensitivity and specificity, whereas baselines exhibited class-recall asymmetry. The generated prospectivity map successfully delineated nine high-probability target zones (I–IX) that align with known mineral occurrences (porphyry, skarn, and hydrothermal veins) and major NW-SE and NE-SW fault systems.

Key Contributions and Significance
The paper claims the following contributions and significance:

1. Direction-Aware Graph Learning: GeoGraphFormer introduces a novel mechanism (GeoRelAttn) that explicitly encodes geological directionality as a learnable inductive bias within a Graph Transformer. This addresses the "isotropic limitation" of previous GNNs and Graph Transformers, enabling the model to preserve orientation-dependent geological signals such as fault-parallel enrichment and structural continuity.
2. Integration of Compositional and Structural Data: The framework effectively combines compositional data analysis (ILR balances) with structural variables (fracture density) and adaptive channel weighting, creating a geologically informed feature space that respects the relative nature of geochemical data.
3. Bridging Geological Knowledge and AI: The study demonstrates that treating direction as a learnable parameter, rather than a fixed coordinate attribute, allows graph-based models to better represent the anisotropic nature of ore-forming systems. This bridges the gap between geological process understanding (e.g., fluid migration along faults) and graph representation learning.
4. Practical Application: The model provides a robust framework for regional polymetallic prospectivity mapping, identifying exploration targets that align with established metallogenic architectures in the Gangdese belt.

Limitations and Modesty of Claims
The authors explicitly acknowledge several limitations:

• Data Size: The labeled dataset is small (234 tiles), which is a constraint for deep learning, though mitigated by ensembling and regularization.
• Generalizability: The model was evaluated on a single metallogenic belt; its transferability to other tectonic settings requires further validation.
• Deposit Specificity: The model predicts binary regional polymetallic prospectivity rather than specific deposit types (e.g., distinguishing porphyry from skarn).
• Validation: The identified high-probability zones are candidate targets requiring independent field mapping and geochemical sampling for confirmation. The outputs are relative prospectivity scores, not calibrated probabilities of confirmed mineralization.

In conclusion, GeoGraphFormer offers a conceptual advancement in mineral prospectivity mapping by shifting from isotropic spatial aggregation to geologically informed, direction-aware relational learning, thereby improving the fidelity of structural signal representation in deep learning models.