# Scientifically-Interpretable Reasoning Network (ScIReN): Discovering Hidden Relationships in the Carbon Cycle and Beyond

arXiv: https://arxiv.org/abs/2506.14054 · HTML: https://mlsanity.com/paper/2506.14054/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 55 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Builds on (most cited first, 18 of 18)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Model-Agnostic Interpretability of Machine Learning](https://mlsanity.com/paper/1606.05386/) (2016)
- [Visualizing the Effects of Predictor Variables in Black Box Supervised Learning Models](https://mlsanity.com/paper/1612.08468/) (2016)
- [Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling](https://mlsanity.com/paper/1710.11431/) (2017)
- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [Challenges in Training PINNs: A Loss Landscape Perspective](https://mlsanity.com/paper/2402.01868/) (2024)
- [Physics Guided RNNs for Modeling Dynamical Systems: A Case Study in Simulating Lake Temperature Profiles](https://mlsanity.com/paper/1810.13075/) (2018)
- [A Simple and Effective Model-Based Variable Importance Measure](https://mlsanity.com/paper/1805.04755/) (2018)
- [Achieving Conservation of Energy in Neural Network Emulators for Climate Modeling](https://mlsanity.com/paper/1906.06622/) (2019)
- [Physics-Guided Architecture (PGA) of Neural Networks for Quantifying Uncertainty in Lake Temperature Modeling](https://mlsanity.com/paper/1911.02682/) (2019)
- [From calibration to parameter learning: Harnessing the scaling effects of big data in geoscientific modeling](https://mlsanity.com/paper/2007.15751/) (2020)
- [Differentiable, learnable, regionalized process-based models with physical outputs can approach state-of-the-art hydrologic prediction accuracy](https://mlsanity.com/paper/2203.14827/) (2022)
- [Automating Crystal-Structure Phase Mapping: Combining Deep Learning with Constraint Reasoning](https://mlsanity.com/paper/2108.09523/) (2021)
- [Hybrid Phenology Modeling for Predicting Temperature Effects on Tree Dormancy](https://mlsanity.com/paper/2501.16848/) (2025)
- [Causal hybrid modeling with double machine learning](https://mlsanity.com/paper/2402.13332/) (2024)
- [Monitoring Vegetation From Space at Extremely Fine Resolutions via Coarsely-Supervised Smooth U-Net](https://mlsanity.com/paper/2207.08022/) (2022)

## Abstract (arXiv)

Soils have potential to mitigate climate change by sequestering carbon from the atmosphere, but the soil carbon cycle remains poorly understood. Scientists have developed process-based models of the soil carbon cycle based on existing knowledge, but they contain numerous unknown parameters and often fit observations poorly. On the other hand, neural networks can learn patterns from data, but do not respect known scientific laws, and are too opaque to reveal novel scientific relationships. We thus propose Scientifically-Interpretable Reasoning Network (ScIReN), a fully-transparent framework that combines interpretable neural and process-based reasoning. An interpretable encoder predicts scientifically-meaningful latent parameters, which are then passed through a differentiable process-based decoder to predict labeled output variables. While the process-based decoder enforces existing scientific knowledge, the encoder leverages Kolmogorov-Arnold networks (KANs) to reveal interpretable relationships between input features and latent parameters, using novel smoothness penalties to balance expressivity and simplicity. ScIReN also introduces a novel hard-sigmoid constraint layer to restrict latent parameters into prior ranges while maintaining interpretability. We apply ScIReN on two tasks: simulating the flow of organic carbon through soils, and modeling ecosystem respiration from plants. On both tasks, ScIReN outperforms or matches black-box models in predictive accuracy, while greatly improving scientific interpretability -- it can infer latent scientific mechanisms and their relationships with input features.