Wang, Ziye, Zuo, Renguang, and Kreuzer, Oliver P. (2025) Uncertainty Quantification of Deep Learning Algorithms for Lithological Mapping. Mathematical Geosciences, 58. pp. 503-531.

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Abstract

Lithological mapping aims to identify, classify, and delineate the boundaries between different rock types in a given area. Recent advances in deep learning algorithms have progressed this process from a traditional manual approach to automated discrimination backed by high-resolution remote sensing data. However, common deep learning algorithms are not explicitly designed to quantify or represent model uncertainty. More importantly, model uncertainty can affect the final predictions because deep learning algorithms are prone to producing overconfident results. In the case of lithological mapping, it is essential not only to estimate the probability of lithological classification but also to measure the level of a model’s confidence. This study integrates three uncertainty modeling approaches—Bayes by backprop, Monte Carlo dropout, and deep ensemble—into a convolutional neural network to quantify the deep learning model uncertainty for lithological mapping. Bayes by backprop employs Bayesian variational inference to approximate probability distributions over network weights to quantify model uncertainty. Monte Carlo dropout captures uncertainty by leveraging dropout as a stochastic approximation to Bayesian inference. Deep ensemble trains multiple independent models with varying parameters and random samples to estimate uncertainty. These approaches are illustrated through lithological mapping studies in the Cuonadong Dome, Tibet, China, using Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) remote sensing data. Several quantitative metrics, including mean, variance, entropy, confidence, expected calibration error, and uncertainty kernel density curves, are employed to rigorously assess and characterize the uncertainties. The results indicate that model uncertainty is primarily concentrated along lithological boundaries and contact zones. Bayes by backprop provides the most reliable uncertainty estimates with low calibration error, while Monte Carlo dropout offers broader uncertainty coverage but suffers from poor calibration. Deep ensemble produces the highest confidence predictions and balances efficiency and performance, although it lacks probabilistic interpretability for uncertainty evaluation. Uncertainty quantification transforms the deterministic deep learning models into more trustworthy tools, thereby avoiding overconfident predictions, improving the reliability of the lithological mapping, and supporting robust geological interpretations and decision-making.

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