# Uncertainty Quantification in Inverse Models in Hydrology

arXiv: https://arxiv.org/abs/2310.02193 · HTML: https://mlsanity.com/paper/2310.02193/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 38 references that are in the map.
- First posted on arXiv 3 Oct 2023.

## Builds on (most cited first, 16 of 16)

- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Concrete Dropout](https://mlsanity.com/paper/1705.07832/) (2017)
- [Maxout Networks](https://mlsanity.com/paper/1302.4389/) (2013)
- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches](https://mlsanity.com/paper/1803.04386/) (2018)
- [Invertible generative models for inverse problems: mitigating representation error and dataset bias](https://mlsanity.com/paper/1905.11672/) (2019)
- [Towards Learning Universal, Regional, and Local Hydrological Behaviors via Machine-Learning Applied to Large-Sample Datasets](https://mlsanity.com/paper/1907.08456/) (2019)
- [Simulation Intelligence: Towards a New Generation of Scientific Methods](https://mlsanity.com/paper/2112.03235/) (2021)
- [Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imaging](https://mlsanity.com/paper/2010.14462/) (2020)
- [Robustness of Bayesian Neural Networks to Gradient-Based Attacks](https://mlsanity.com/paper/2002.04359/) (2020)
- [Statistical Guarantees for the Robustness of Bayesian Neural Networks](https://mlsanity.com/paper/1903.01980/) (2019)
- [Solving Inverse Problems with a Flow-based Noise Model](https://mlsanity.com/paper/2003.08089/) (2020)
- [Fine-grained Recognition in the Wild: A Multi-Task Domain Adaptation Approach](https://mlsanity.com/paper/1709.02476/) (2017)
- [PID-GAN: A GAN Framework based on a Physics-informed Discriminator for Uncertainty Quantification with Physics](https://mlsanity.com/paper/2106.02993/) (2021)
- [Robust Inverse Framework using Knowledge-guided Self-Supervised Learning: An application to Hydrology](https://mlsanity.com/paper/2109.06429/) (2021)
- [Probabilistic Inverse Modeling: An Application in Hydrology](https://mlsanity.com/paper/2210.06213/) (2022)

## Abstract (arXiv)

In hydrology, modeling streamflow remains a challenging task due to the limited availability of basin characteristics information such as soil geology and geomorphology. These characteristics may be noisy due to measurement errors or may be missing altogether. To overcome this challenge, we propose a knowledge-guided, probabilistic inverse modeling method for recovering physical characteristics from streamflow and weather data, which are more readily available. We compare our framework with state-of-the-art inverse models for estimating river basin characteristics. We also show that these estimates offer improvement in streamflow modeling as opposed to using the original basin characteristic values. Our inverse model offers 3% improvement in R2 for the inverse model (basin characteristic estimation) and 6% for the forward model (streamflow prediction). Our framework also offers improved explainability since it can quantify uncertainty in both the inverse and the forward model. Uncertainty quantification plays a pivotal role in improving the explainability of machine learning models by providing additional insights into the reliability and limitations of model predictions. In our analysis, we assess the quality of the uncertainty estimates. Compared to baseline uncertainty quantification methods, our framework offers 10% improvement in the dispersion of epistemic uncertainty and 13% improvement in coverage rate. This information can help stakeholders understand the level of uncertainty associated with the predictions and provide a more comprehensive view of the potential outcomes.