# QDeepGR4J: Quantile-based ensemble of deep learning and GR4J hybrid rainfall-runoff models for extreme flow prediction with uncertainty quantification

arXiv: https://arxiv.org/abs/2510.05453 · HTML: https://mlsanity.com/paper/2510.05453/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 88 references that are in the map.
- First posted on arXiv 6 Oct 2025.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Methods for Interpreting and Understanding Deep Neural Networks](https://mlsanity.com/paper/1706.07979/) (2017)
- [Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge](https://mlsanity.com/paper/1711.07970/) (2017)
- [Evaluation of deep learning models for multi-step ahead time series prediction](https://mlsanity.com/paper/2103.14250/) (2021)
- [Neural Networks for Extreme Quantile Regression with an Application to Forecasting of Flood Risk](https://mlsanity.com/paper/2208.07590/) (2022)
- [Physics-Aware Gaussian Processes in Remote Sensing](https://mlsanity.com/paper/2012.07986/) (2020)
- [Review of deep learning models for crypto price prediction: implementation and evaluation](https://mlsanity.com/paper/2405.11431/) (2024)
- [Quantile deep learning models for multi-step ahead time series prediction](https://mlsanity.com/paper/2411.15674/) (2024)

## Abstract (arXiv)

Conceptual rainfall-runoff models aid hydrologists and climate scientists in modelling streamflow to inform water management practices. Recent advances in deep learning have unravelled the potential for combining hydrological models with deep learning models for better interpretability and improved predictive performance. In our previous work, we introduced DeepGR4J, which enhanced the GR4J conceptual rainfall-runoff model using a deep learning model to serve as a surrogate for the routing component. DeepGR4J had an improved rainfall-runoff prediction accuracy, particularly in arid catchments. Quantile regression models have been extensively used for quantifying uncertainty while aiding extreme value forecasting. In this paper, we extend DeepGR4J using a quantile regression-based ensemble learning framework to quantify uncertainty in streamflow prediction. We also leverage the uncertainty bounds to identify extreme flow events potentially leading to flooding. We further extend the model to multi-step streamflow predictions for uncertainty bounds. We design experiments for a detailed evaluation of the proposed framework using the CAMELS-Aus dataset. The results show that our proposed Quantile DeepGR4J framework improves the predictive accuracy and uncertainty interval quality (interval score) compared to baseline deep learning models. Furthermore, we carry out flood risk evaluation using Quantile DeepGR4J, and the results demonstrate its suitability as an early warning system.