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Abstract <p>Accurately predicting the spatiotemporal evolution of heavy metals (HMs) in soil is crucial for controlling environmental risks and providing early warnings for food safety. To address the unclear nonlinear diffusion patterns of HMs in soil, this study proposes a hybrid physics–data-driven predictive framework that integrates physical transport mechanisms with complex network theory. Taking the “soil–Cd–wheat” system as a case study, soil sampling locations are represented as network nodes, and spatially adjacent sites are connected as edges to construct a soil HM propagation network. Based on this, a physics-informed propagation dynamics model is developed to characterize the nonlinear transport behavior of Cd between network nodes. A meta-learning strategy is further incorporated to optimize key physical and empirical parameters, resulting in a hybrid prediction model termed PICN-MAML. Experimental results show that PICN-MAML outperforms other benchmark models, achieving a coefficient of determination of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>R</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>=0.9847. Global sensitivity analysis indicates that molecular diffusion and advection processes are the dominant factors influencing the spatiotemporal distribution of Cd concentrations. In addition, a comprehensive risk assessment combining carcinogenic and non-carcinogenic health risks with node importance and spreading capacity is conducted, enabling the identification of both currently high-risk and potentially high-risk nodes and supporting targeted early warning and risk management strategies.</p> Graphical abstract <p></p>

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A hybrid physics–data-driven predictive framework for early warning and risk assessment of soil heavy metal pollution using complex networks

  • 期刊论文

  • 发表日期：

    2026年8月3日

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  • Xiaoyu Cui,
  • Luming Cai,
  • Zhiyao Zhao,
  • Ding Wang

摘要

Abstract

Accurately predicting the spatiotemporal evolution of heavy metals (HMs) in soil is crucial for controlling environmental risks and providing early warnings for food safety. To address the unclear nonlinear diffusion patterns of HMs in soil, this study proposes a hybrid physics–data-driven predictive framework that integrates physical transport mechanisms with complex network theory. Taking the “soil–Cd–wheat” system as a case study, soil sampling locations are represented as network nodes, and spatially adjacent sites are connected as edges to construct a soil HM propagation network. Based on this, a physics-informed propagation dynamics model is developed to characterize the nonlinear transport behavior of Cd between network nodes. A meta-learning strategy is further incorporated to optimize key physical and empirical parameters, resulting in a hybrid prediction model termed PICN-MAML. Experimental results show that PICN-MAML outperforms other benchmark models, achieving a coefficient of determination of \(R^2\) R 2 =0.9847. Global sensitivity analysis indicates that molecular diffusion and advection processes are the dominant factors influencing the spatiotemporal distribution of Cd concentrations. In addition, a comprehensive risk assessment combining carcinogenic and non-carcinogenic health risks with node importance and spreading capacity is conducted, enabling the identification of both currently high-risk and potentially high-risk nodes and supporting targeted early warning and risk management strategies.

Graphical abstract