Interpretable Network Framework for Predicting the Spatial Distribution of Chromium in Soil

Xinping Luo (), Wei Luo, Jing Hao, Yuchen Zhu and Xiangke Kong
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Xinping Luo: Comprehensive Survey Command Center for Natural Resources, China Geological Survey, Beijing 100055, China
Wei Luo: Key Laboratory of Coupling Process and Effect of Natural Resources Elements, Ministry of Natural Resources, Beijing 100055, China
Jing Hao: Comprehensive Survey Command Center for Natural Resources, China Geological Survey, Beijing 100055, China
Yuchen Zhu: Institute of Hydrogeology and Environmental Geology, CAGS, Chinese Academy of Geological Sciences, Xiamen 361000, China
Xiangke Kong: Institute of Hydrogeology and Environmental Geology, CAGS, Chinese Academy of Geological Sciences, Xiamen 361000, China

Sustainability, 2025, vol. 17, issue 14, 1-19

Abstract: Investigating the spatial distribution of chromium (Cr) in soil is essential for understanding Cr pollution and accurately assessing associated environmental risks. However, field sampling is challenging due to limited sampling points, and the spatial distribution of Cr is affected by multiple complex environmental covariates, thereby restricting model development and prediction accuracy. This study selected the Chizhou–Xuancheng border area in southern Anhui Province as the research region and collected 2035 data points. Machine learning models, including AdaBoost, GBDT, XGBoost, and MLP, were employed to predict Cr concentrations in conjunction with environmental covariates. To address the challenges of sparse sampling data and complex data relationships for Cr prediction, the PHMS-Transformer model is proposed. Featuring a shallow encoder design, configurable pooling strategies, and a lightweight structure, the model significantly reduces the number of parameters and alleviates overfitting under sparse sampling conditions, while the incorporation of multi-head self-attention mechanisms captures complex nonlinear relationships among multi-source environmental variables relevant to Cr. To further enhance model interpretability for Cr prediction, the SHAP model was applied to identify key factors influencing Cr distribution. Comprehensive comparisons indicate that the PHMS-Transformer model achieves superior performance in predicting Cr, demonstrating high accuracy and generalization capability, with clear advantages over traditional methods. These findings offer valuable insights for soil environmental protection and Cr pollution control and possess significant theoretical and practical implications. Soil Cr pollution represents a global environmental challenge, where achieving accurate predictions for Cr is particularly crucial yet difficult in regions with constrained data accessibility. The lightweight, high-precision, and interpretable PHMS-Transformer framework proposed in this study provides an effective technical solution to the widespread challenges of sample sparsity and model complexity inherent in predicting the spatial distribution of soil Cr globally. Therefore, this work offers significant reference value for advancing global soil environmental risk assessment and Cr pollution remediation efforts.

Keywords: soil heavy metals; machine learning; PHMS-Transformer; SHAP (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2025
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