• A novel SEM-HNN architecture was developed by transposing SEM causal topologies into neural networks. • An adaptive fusion mechanism is introduced to dynamically balance structural priors with data-driven learning. • SEM-HNN outperforms conventional integration strategies and provides superior predictive stability. • The model exhibits higher architectural efficiency than conventional pure neural networks. • The hybrid design ensures robust SOC prediction even with imperfect prior knowledge. Soil organic carbon (SOC) plays an important role in the global carbon cycle, yet its pronounced spatial heterogeneity driven by multiple environmental factors makes accurate prediction challenging. Knowledge-guided machine learning has gained significant attention as a promising solution due to that purely data-driven approaches often lack interpretability. Structural equation modeling (SEM) offers knowledge by quantifying the influence of environmental drivers on soil property spatial patterns, motivating its integration with machine learning. However, existing SEM-machine learning integration approaches, typically through input augmentation or structure constraints, often assume prior structures are exhaustive, limiting model adaptability and failing to capture the intrinsic complexity and non-linear patterns of environmental data. To address this limitation, we developed an SEM-Guided Hybrid Neural Network (SEM-HNN), which transposes the structural topology of SEM into a modular neural architecture, dynamically fused with a parallel, unconstrained neural branch. Validation on cropland SOC prediction in East China demonstrates that SEM-HNN outperforms both purely data-driven models (the unconstrained neural network) and conventional SEM-integration approaches (i.e., Feature Augmentation and Sample Weighting). Specifically, it achieved higher accuracy (mean R 2 of 0.554) with lower predictive variability (SD = 0.137 vs 0.163 for pure neural network). Notably, the SEM-HNN exhibits high architectural efficiency, attaining comparable or superior performance with fewer hidden neurons than pure neural networks. Furthermore, the hybrid design ensures robustness to incomplete prior knowledge, maintaining performance even when the SEM’s intrinsic explanatory power is limited. Overall, this study offers a novel and robust knowledge-guided machine learning approach for spatial prediction of soil properties.
Guo et al. (Fri,) studied this question.