Enhancing Lithological Mapping with Spatially Constrained Bayesian
  Network (SCB-Net): An Approach for Field Data-Constrained Predictions with
  Uncertainty Evaluation
Victor Silva dos Santos Erwan Gloaguen Shiva Tirdad
Geological maps are an extremely valuable source of information for the Earth
sciences. They provide insights into mineral exploration, vulnerability to
natural hazards, and many other applications. These maps are created using
numerical or conceptual models that use geological observations to extrapolate
data. Geostatistical techniques have traditionally been used to generate
reliable predictions that take into account the spatial patterns inherent in
the data. However, as the number of auxiliary variables increases, these
methods become more labor-intensive. Additionally, traditional machine learning
methods often struggle with spatially correlated data and extracting valuable
non-linear information from geoscientific datasets. To address these
limitations, a new architecture called the Spatially Constrained Bayesian
Network (SCB-Net) has been developed. The SCB-Net aims to effectively exploit
the information from auxiliary variables while producing spatially constrained
predictions. It is made up of two parts, the first part focuses on learning
underlying patterns in the auxiliary variables while the second part integrates
ground-truth data and the learned embeddings from the first part. Moreover, to
assess model uncertainty, a technique called Monte Carlo dropout is used as a
Bayesian approximation. The SCB-Net has been applied to two selected areas in
northern Quebec, Canada, and has demonstrated its potential in generating
field-data-constrained lithological maps while allowing assessment of
prediction uncertainty for decision-making. This study highlights the promising
advancements of deep neural networks in geostatistics, particularly in handling
complex spatial feature learning tasks, leading to improved spatial information
techniques.