This paper highlights the importance of understanding the soil carbon cycle for climate change mitigation, highlighting the limitations of existing mathematical process-based models (unknown parameters, inaccurate fit to observations) and neural networks (ignoring scientific laws, black-box nature). Therefore, we propose a novel framework, Scientifically-Interpretable Reasoning Network (ScIReN), that combines interpretable neural networks and process-based reasoning. ScIReN predicts scientifically meaningful latent parameters through an interpretable encoder (using Kolmogorov-Arnold Networks) and then passes these parameters to a differentiable, process-based decoder to predict output variables. A novel smoothness penalty and hard sigmoid constraint layer are employed to incorporate prior scientific knowledge, improving prediction accuracy and interpretability. ScIReN is applied to two tasks: soil organic carbon flux simulation and plant ecosystem respiration modeling, demonstrating higher prediction accuracy and scientific interpretability than black-box neural networks. We demonstrate that ScIReN can infer relationships between potential scientific mechanisms and input features.
