A study of Universal ODE approaches to predicting soil organic carbon

Abstract

Soil Organic Carbon (SOC) is a foundation of soil health and global climate resilience, yet its prediction remains difficult because of intricate physical, chemical, and biological processes. In this study, we explore a Scientific Machine Learning (SciML) framework built on Universal Differential Equations (UDEs) to forecast SOC dynamics across soil depth and time. UDEs blend mechanistic physics, such as advection diffusion transport, with neural networks that learn nonlinear microbial production and respiration. Using synthetic datasets, we systematically evaluated six experimental cases, progressing from clean, noise free benchmarks to stress tests with high (35%) multiplicative, spatially correlated noise. Our results highlight both the potential and limitations of the approach. In noise free and moderate noise settings, the UDE accurately reconstructed SOC dynamics. In clean terminal profile at 50 years (Case 4) achieved near perfect fidelity, with MSE = 1.6e-5, and R2 = 0.9999. Case 5, with 7% noise, remained robust (MSE = 3.4e-6, R2 = 0.99998), capturing depth wise SOC trends while tolerating realistic measurement uncertainty. In contrast, Case 3 (35% noise at t = 0) showed clear evidence of overfitting: the model reproduced noisy inputs with high accuracy but lost generalization against the clean truth (R2 = 0.94). Case 6 (35% noise at t = 50) collapsed toward overly smooth mean profiles, failing to capture depth wise variability and yielding negative R2, underscoring the limits of standard training under severe uncertainty. These findings suggest that UDEs are well suited for scalable, noise tolerant SOC forecasting, though advancing toward field deployment will require noise aware loss functions, probabilistic modelling, and tighter integration of microbial dynamics.