Enhancing Lithological Mapping with Spatially Constrained Bayesian Network (SCB-Net): An Approach for Field Data-Constrained Predictions with Uncertainty Evaluation

TL;DR

SCB-Net tackles predictive lithological mapping under field-data constraints by fusing auxiliary remote-sensing data with sparse ground-truth through a two-part U-Net architecture and Bayesian uncertainty via Monte Carlo dropout. The method employs two Attention Residual U-Nets (W-net inspired) to learn from auxiliary data and fuse embeddings with sparse ground-truth masks, augmented by a custom loss that includes a dilation operator to capture spatial dependencies. It demonstrates effectiveness on two northern Quebec study areas, achieving improved per-class accuracy under spatial constraints and providing uncertainty maps, with transfer learning enabling rapid adaptation to a new area. This work showcases how integrating geostatistical intent with deep learning and probabilistic reasoning can enhance regional lithological mapping and support uncertainty-aware decision-making.

Abstract

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.

Figures (14)

• Figure 1: Our proposed architecture for obtaining field-data constrained predictions. The model is basically composed of two Attention Res-Unets, which are responsible for extracting features from the auxiliary data and fusing them with the sparse probability masks.
• Figure 2: The northeast area is divided into spatial blocks, each measuring 15x15 pixels. The training set is represented by pink blocks, while the testing set is represented by orange blocks. The green zone is reserved for validation purposes. You may notice some dark-blue blocks which contain no field-samples.
• Figure 3: Study areas in the province of Quebec. The northeast area is highlighted in green, while the northern area is highlighted in red.
• Figure 4: Remote sensing dataset used as auxiliary variables for lithology prediction.
• Figure 5: Field data available in the northeast study area.