Explainable Neuro-Symbolic Learning for Mohs Hardness Prediction in Mining and Mineral Processing

Abstract

Predicting Mohs hardness from mineralogical information is still a challenging task because of the complex and nonlinear relationship between mineral composition and hardness properties. Traditional machine learning (ML) and deep learning (DL) strategies have been used to address this study, exploiting mineralogical attributes for prediction. Conversely, these techniques are frequently highly dependent on large labeled datasets, struggle to generalize over distinct mineral categories, and face challenges in extracting subtle physicochemical interactions and delivering interpretable predictions. This study presents an Explainable Deep Representation Learning Framework based on Mohs Hardness Prediction (XDRL-MHP). The primary objective of this work is to predict Mohs hardness using mineralogical properties by modeling mineral composition and structural characteristics. The proposed model employs mRMR for feature selection to identify the most informative physicochemical attributes. A physicochemical representation constructed using atomic interaction mapping, periodic table relationship encoding, chemical affinity representation, and molecular dependency construction to capture complex mineral relationships. Besides, a neuro-symbolic hybrid architecture is designed by integrating a capsule network for hierarchical mineral pattern learning, a neural tensor network for atomic relationship modeling, and a symbolic reasoning layer for rule-guided mineral intelligence. In addition, an explainable neuro-artificial intelligence technique incorporated to improve model interpretability and insight into predictions. The model is trained using the AdaBelief optimizer with quantile loss for ensure stable convergence and precise Mohs hardness prediction. The XDRL-MHP method validated utilizing the Comprehensive Database of Minerals, comprising 3,112 mineral instances with 140 mineralogical and physicochemical features. The simulation analysis of the XDRL-MHP model is performed using the Comprehensive Database of Minerals. Extensive comparative results show the effective performance of the XDRL-MHP model with an RMSE of 0.1140 over recent state-of-the-art models.