A Physically Constrained Variational Autoencoder for Geochemical Pattern Recognition

Quantification and recognition of geochemical patterns are extremely important for geochemical prospecting and can facilitate a better understanding of regional metallogenesis. Recognition of such patterns with deep learning (DL) algorithms has attracted considerable attention, as these algorithms can generally extract high-level geochemical features and thus create models in which geochemical patterns are fully exploited. These DL algorithms are usually constructed to be compatible and consistent with the underlying data, but their interpretability and pertinent physical constraints (such as granitic intrusions related to magmatic-hydrothermal mineralization) are generally overlooked. This paper introduces a physically constrained variational autoencoder (VAE) architecture to identify geochemical patterns associated with tungsten polymetallic mineralization. We first identify physical constraints from geological characteristics and metallogenic regulation via the methods of fry analysis, standard deviation ellipses, and fractal analysis to reveal the controlling function of granitic intrusions on mineralization. Subsequently, we construct the physical constraints based on the nonlinear controlling function and add the geological constraints into the VAE loss function as a penalty term. After optimization of the network parameters, the well-trained physically constrained VAE architecture can recognize the geochemical anomaly patterns that the conventional VAE cannot. These extracted geochemical anomaly patterns generally show a strong spatial relationship with the granitic intrusions. In addition, the performance measures involving the receiver operating characteristic curve and success-rate further indicate that the generalization accuracy of the conventional VAE can be enhanced via physics-based regularization. These results suggest that the proposed physically constrained VAE, which integrates physical knowledge into the VAE loss function, not only improves the geochemical pattern recognition performance but also demonstrates consistency with geological and physical domain knowledge.