# CauSTream: Causal Spatio-Temporal Representation Learning for Streamflow Forecasting

arXiv: https://arxiv.org/abs/2512.16046 · HTML: https://mlsanity.com/paper/2512.16046/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 35 references that are in the map.
- First posted on arXiv 18 Dec 2025.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [On the Identifiability of Nonlinear ICA: Sparsity and Beyond](https://mlsanity.com/paper/2206.07751/) (2022)
- [A trans-disciplinary review of deep learning research for water resources scientists](https://mlsanity.com/paper/1712.02162/) (2017)
- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Learning General Causal Structures with Hidden Dynamic Process for Climate Analysis](https://mlsanity.com/paper/2501.12500/) (2025)
- [Spatio-temporal Causal Learning for Streamflow Forecasting](https://mlsanity.com/paper/2411.17937/) (2024)

## Abstract (arXiv)

Streamflow forecasting is crucial for water resource management and risk mitigation. While deep learning models have achieved strong predictive performance, they often overlook underlying physical processes, limiting interpretability and generalization. Recent causal learning approaches address these issues by integrating domain knowledge, yet they typically rely on fixed causal graphs that fail to adapt to data. We propose CauStream, a unified framework for causal spatiotemporal streamflow forecasting. CauSTream jointly learns (i) a runoff causal graph among meteorological forcings and (ii) a routing graph capturing dynamic dependencies across stations. We further establish identifiability conditions for these causal structures under a nonparametric setting. We evaluate CauSTream on three major U.S. river basins across three forecasting horizons. The model consistently outperforms prior state-of-the-art methods, with performance gaps widening at longer forecast windows, indicating stronger generalization to unseen conditions. Beyond forecasting, CauSTream also learns causal graphs that capture relationships among hydrological factors and stations. The inferred structures align closely with established domain knowledge, offering interpretable insights into watershed dynamics. CauSTream offers a principled foundation for causal spatiotemporal modeling, with the potential to extend to a wide range of scientific and environmental applications.