Uncertainty quantification of deep learning model for mineral prospectivity mapping

1. Overview This repository provides the Python code used to implement the uncertainty quantification framework described in the associated manuscript. The framework integrates data uncertainty, model uncertainty, and prediction uncertainty within a deep learning–based mineral prospectivity mapping (MPM) workflow. The proposed framework consists of three main components: (1) Data uncertainty quantification Geological evidence layers are simulated using stochastic simulation to represent data uncertainties caused by sparse sampling and subjective geological interpretation. (2) Model uncertainty quantification A Bayesian convolutional neural network (CNN) with Monte Carlo Dropout is used to capture model uncertainty in parameters variability. (3) Prediction uncertainty estimation Multiple stochastic predictions are generated and aggregated to estimate prediction uncertainty, providing spatial uncertainty measures for MPM. 2. Main steps (1) Evidence layers simulation Continuous Data Uncertainty Modeling Script: Continuous_data_uncertainty_modeling.py This module models uncertainty in continuous geological evidence layers (e.g., faults, intrusions, and formations). Main functions: Weighting Curve Simulation Generates multiple distance-decay weighting curves under different uncertainty thresholds. Evidence Layer Weighting Applies the simulated weighting functions to each pixel of a geological layer, producing an ensemble of weighted evidence layers. Inputs: Geological evidence layer (e.g., geological_layer_fault.tif) Weight coefficient Number of simulations Outputs: Figure showing multiple simulated weighting curves Ensemble of weighted evidence layers (.mat format) Discrete Data Uncertainty Modeling Script: Discrete_data_uncertainty_modeling.py This module models uncertainty in geochemical and geophysical evidence layers using the Direct Sampling (DS) algorithm. Inputs: Conditioning data (au_point.tif) Training image (au_ti.tif) Number of simulations Outputs: Ensemble of simulated evidence layers (.mat format) (2) Data uncertainty quantification This component evaluates how uncertainty in evidence layers propagates to MPM. Inputs: Simulated evidence layers (Simulated_evidence_layers.mat) Mineral deposit labels (deposit.tif) # Simulated evidence layers.mat is an n-dimensional cell array consisting of n simulation realizations, each with dimensions of X × Y × Z. Procedure: Generate training samples using sliding windows Train CNN models for each stochastic simulation Predict mineral prospectivity for each simulation Compute uncertainty metrics: mean prediction, variance, entropy Outputs: uncertainty_mean.tif uncertainty_variance.tif uncertainty_entropy.tif (3) Model uncertainty quantification This component evaluates uncertainty associated with model parameters using Bayesian CNNs with Monte Carlo Dropout. Inputs: Integrated evidence layers (evidence layer.tif) Mineral deposit labels (deposit.tif) # evidence layers.tif is 44-evidence layers combining fault (geological layer_fault.tif), intrusion (geological layer_intrusion.tif), formation (geological layer_taihua formation.tif and geological layer_xionger formation.tif), geophysical (geophysical aeromagnetic layer.tif), and 39-geochemical (geochemical layer.tif) layers, each with dimensions of X × Y × Z. Procedure: Generate training samples using sliding windows Train a Bayesian CNN with MC Dropout Predict mineral prospectivity for each simulation Compute uncertainty metrics: mean prediction, variance, entropy Outputs: uncertainty_mean.tif uncertainty_variance.tif uncertainty_entropy.tif (4) Prediction uncertainty estimation This component combines data uncertainty and model uncertainty to quantify the overall uncertainty of MPM. Inputs: Simulated evidence layers (Simulated_evidence_layers.mat) Mineral deposit labels (deposit.tif) # Simulated evidence layers.mat is an n-dimensional cell array consisting of n simulation realizations, each with dimensions of X × Y × Z. Procedure: Generate training samples using sliding windows Train a CNN model for each stochastic simulation Predict mineral prospectivity for each simulation Compute uncertainty metrics: mean prediction, variance, entropy Outputs: uncertainty_mean.tif uncertainty_variance.tif uncertainty_entropy.tif 3. Software Requirements The code was developed using the following environment: Python 3.9 TensorFlow 2.x NumPy SciPy Pandas Matplotlib scikit-learn GDAL 4. Author & Contact Author: Ziye Wang Affiliation: China University of Geosciences Contact: ziyewang@cug.edu.cn