# Multi-Modal Spatio-Temporal Graph Neural Network with Mixture of Experts for Soil Organic Carbon Prediction

arXiv: https://arxiv.org/abs/2606.16580 · HTML: https://mlsanity.com/paper/2606.16580/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 30 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Builds on (most cited first, 15 of 15)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Scaling Vision with Sparse Mixture of Experts](https://mlsanity.com/paper/2106.05974/) (2021)
- [Prithvi-EO-2.0: A Versatile Multi-Temporal Foundation Model for Earth Observation Applications](https://mlsanity.com/paper/2412.02732/) (2024)
- [AlphaEarth Foundations: An embedding field model for accurate and efficient global mapping from sparse label data](https://mlsanity.com/paper/2507.22291/) (2025)
- [TerraMind: Large-Scale Generative Multimodality for Earth Observation](https://mlsanity.com/paper/2504.11171/) (2025)
- [Relational Graph Attention Networks](https://mlsanity.com/paper/1904.05811/) (2019)
- [Positional Encoder Graph Neural Networks for Geographic Data](https://mlsanity.com/paper/2111.10144/) (2021)
- [Soil Organic Carbon Estimation from Climate-related Features with Graph Neural Network](https://mlsanity.com/paper/2311.15979/) (2023)
- [Chance Constrained Stochastic Optimal Control for Arbitrarily Disturbed LTI Systems Via the One-Sided Vysochanskij-Petunin Inequality](https://mlsanity.com/paper/2303.12295/) (2023)

## Abstract (arXiv)

Top-soil organic carbon (SOC) prediction is fundamental to agricultural sustainability, land use policy and fertilization planning. Existing approaches face two limitations: they pair hand-crafted covariates with classical ML or single-modal deep models that miss rich spectral and temporal information, and grid-based architectures ignore the irregular spatial structure of field measurements. We introduce SpTGNN, a multi-modal spatio-temporal graph neural network addressing both. SpTGNN represents soil measurements as nodes in a heterogeneous graph with three edge types (spatial proximity, spectral similarity, elevation), and applies relational graph attention to learn separate patterns per relation. A fine-tuned TerraMind encoder extracts node features from Sentinel-2, Sentinel-1 and DEM signals, combined with per-sample environmental covariates and learned positional and temporal embeddings. A sparse Mixture-of-Experts module fuses the four streams via top-k routing. Uncertainty is captured by pairing heteroscedastic regression (aleatoric) with deep ensembles (epistemic), and a Moran's I penalty regularizes spatial autocorrelation. We evaluate on a global SOC corpus split into three regional instances (~49k samples globally, Africa ~26k, Europe ~14k). Our 5-member deep ensemble reports R2=0.762, RMSE =3.51±0.48 g/kg and MAPE =22.9% on the Africa test split, improving over a tabular XGBoost baseline; the best single checkpoint reaches validation R2=0.864. Ablations confirm the heterogeneous graph, MoE fusion and fine-tuned backbone each contribute substantively, and the ensemble UQ stack achieves post-calibration ECE of 0.031 (hybrid) and 0.026 (β-NLL). To our knowledge, this is the first framework to unify foundation-model feature extraction, heterogeneous graph attention and decomposed uncertainty quantification for SOC estimation.