Robust Prediction of Subsoil (40–100 cm) SOC Stocks Using a Hybrid Linear–Neural Model

Accurate prediction of subsoil soil organic carbon (SOC) stocks remains challenging due to strong spatial heterogeneity, limited sampling at depth, and model instability across data partitions. In a recent analysis, we identified a linear relationship to predict SOC stocks in the 40–100 cm interval from the SOC stocks at 30–40 cm. Here, we benchmark the linear model against a new neural architecture designed to improve robustness across cross-validation folds while maintaining a transparent baseline.

We propose LCR-Net, a hybrid model that embeds a trainable linear baseline within a neural network and learns an additive, soft cluster-specific residual. The model takes SOC stocks from 0 to 40 cm as inputs, generates a global latent scalar to support gating, and assigns each sample to clusters via a softmax mechanism; predictions are given by the linear baseline plus a gated residual term. This design explicitly retains a linear component while allowing structured, data-driven corrections that can capture latent regimes in SOC depth-profile relationships.

Across three fixed cross-validation folds, the linear regression achieved an RMSE of 18.52 ± 0.65 Mg ha⁻¹, whereas LCR-Net achieved a comparable RMSE of 18.96 ± 0.09 Mg ha⁻¹. While mean predictive accuracy was similar, LCR-Net substantially reduced the fold-to-fold variability of RMSE, indicating improved stability to split perturbations, an important requirement for reproducible subsoil SOC stock estimation. These results suggest that combining a constrained linear prior with soft cluster-based residual learning can stabilize predictions of deep SOC stocks without sacrificing overall accuracy.