# Hierarchical Conditional Multi-Task Learning for Streamflow Modeling

arXiv: https://arxiv.org/abs/2410.14137 · HTML: https://mlsanity.com/paper/2410.14137/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 31 references that are in the map.
- First posted on arXiv 18 Oct 2024.

## Builds on (most cited first, 7 of 7)

- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Towards Learning Universal, Regional, and Local Hydrological Behaviors via Machine-Learning Applied to Large-Sample Datasets](https://mlsanity.com/paper/1907.08456/) (2019)
- [Physics Guided RNNs for Modeling Dynamical Systems: A Case Study in Simulating Lake Temperature Profiles](https://mlsanity.com/paper/1810.13075/) (2018)
- [Physics Guided Machine Learning Methods for Hydrology](https://mlsanity.com/paper/2012.02854/) (2020)
- [Rainfall-Runoff Prediction at Multiple Timescales with a Single Long Short-Term Memory Network](https://mlsanity.com/paper/2010.07921/) (2020)
- [Mini-Batch Learning Strategies for modeling long term temporal dependencies: A study in environmental applications](https://mlsanity.com/paper/2210.08347/) (2022)
- [Message Propagation Through Time: An Algorithm for Sequence Dependency Retention in Time Series Modeling](https://mlsanity.com/paper/2309.16882/) (2023)

## Built on by (most cited first, 1 of 1)

- [Foundation Models for Environmental Science: A Survey of Emerging Frontiers](https://mlsanity.com/paper/2504.04280/) (2025)

## Abstract (arXiv)

Streamflow, vital for water resource management, is governed by complex hydrological systems involving intermediate processes driven by meteorological forces. While deep learning models have achieved state-of-the-art results of streamflow prediction, their end-to-end single-task learning approach often fails to capture the causal relationships within these systems. To address this, we propose Hierarchical Conditional Multi-Task Learning (HCMTL), a hierarchical approach that jointly models soil water and snowpack processes based on their causal connections to streamflow. HCMTL utilizes task embeddings to connect network modules, enhancing flexibility and expressiveness while capturing unobserved processes beyond soil water and snowpack. It also incorporates the Conditional Mini-Batch strategy to improve long time series modeling. We compare HCMTL with five baselines on a global dataset. HCMTL's superior performance across hundreds of drainage basins over extended periods shows that integrating domain-specific causal knowledge into deep learning enhances both prediction accuracy and interpretability. This is essential for advancing our understanding of complex hydrological systems and supporting efficient water resource management to mitigate natural disasters like droughts and floods.