Soil science-informed neural networks for soil organic carbon density modelling under scarce bulk density data

Abstract. Soil organic carbon (SOC) density is a key variable for quantifying soil carbon stocks, yet its modelling is challenged by sparse and inconsistent measurements of bulk density and coarse fragments relative to SOC content. Conventional digital soil mapping approaches typically model SOC density as a single target variable, thereby underutilising abundant SOC content data and overlooking physical relationships among soil properties. This study evaluates a soil science-informed neural network for SOC density prediction that explicitly constrains the SOC–BD relationship, and compares it with univariate and multivariate neural network architectures. Across sparsely sampled target variables, including SOC density, bulk density, and coarse fragments, the soil science-informed model achieves comparable or slightly improved prediction accuracy relative to multivariate and univariate models. Although it yields lower accuracy for SOC content, the soil science-informed model better preserves physically plausible SOC–BD joint distributions and generates smoother, more temporally stable SOC density trajectories. Overall, the results demonstrate that incorporating soil physical constraints into machine learning models adds value beyond univariate accuracy, improving robustness, plausibility, and temporal coherence of SOC density predictions under sparse data conditions. Moreover, the latent parameters inferred by the soil science-informed model improve model interpretability and offer additional soil science relevant insights beyond predictive accuracy.