Mineral Prospectivity Mapping and Uncertainty Quantification Based on Bayesian Physics-Informed Neural Networks——A Case Study of Cu-Ni Deposits in Eastern Tianshan

Mineral resource prediction is a critical component of geological exploration. Traditional machine learning methods face challenges such as overfitting and lack of physical interpretability when processing small-sample, high-dimensional geological data. In this study, we apply the Bayesian Physics-Informed Neural Network (B-PINN) method to embed the physical laws governing geological mineralization processes into a deep learning framework, enabling mineral resource prediction and uncertainty quantification in the Eastern Tianshan copper-nickel metallogenic belt. The B-PINN model employs an 8-layer Bayesian fully connected network with 256 neurons per layer, taking normalized spatial coordinates as inputs and outputting concentrations of four elements (Cu, Ni, Co, and Cr) along with a comprehensive mineralization probability. The model incorporates a steady-state diffusion equation with source terms (D·∇2C + S = 0) as physical constraints, where the source term S comprises fault-related and intrusive rock body-related components that simulate fault-controlled and intrusion-controlled mineralization mechanisms, respectively. The training process utilizes a multi-objective loss function containing nine terms and a three-stage progressive strategy, achieving stable convergence within 10,000 epochs. The prediction results indicate that the mean concentrations of Cu, Ni, Co, and Cr are 22.03, 16.42, 8.94, and 39.37 ppm, respectively. The Cu-Ni-Co elements exhibit strong positive correlations (r = 0.78-0.85), consistent with the geochemical characteristics of magmatic copper-nickel sulfide deposits. The spatial distribution of mineralization probability displays distinct fault-controlled features, with high-probability zones (P > 0.7) accounting for 2.2% of the study area and distributed along NE-trending fault zones. The model achieves 100% classification accuracy for known mineral occurrences and background areas, with mean mineralization probabilities of 0.79 and 0.27 for positive and negative samples, respectively, demonstrating excellent separability. Compared with the Weights of Evidence (WofE) method, the B-PINN model exhibits higher mineral deposit capture efficiency and better spatial continuity, while simultaneously providing both predicted values and uncertainty estimates, thereby offering more comprehensive information to support exploration decision-making.