# Probabilistic Inverse Modeling: An Application in Hydrology

arXiv: https://arxiv.org/abs/2210.06213 · HTML: https://mlsanity.com/paper/2210.06213/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 58 references that are in the map.
- First posted on arXiv 12 Oct 2022.

## Builds on (most cited first, 30 of 31)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Adversarial Training for Free!](https://mlsanity.com/paper/1904.12843/) (2019)
- [Overfitting in adversarially robust deep learning](https://mlsanity.com/paper/2002.11569/) (2020)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Measuring Robustness to Natural Distribution Shifts in Image Classification](https://mlsanity.com/paper/2007.00644/) (2020)
- [TextBugger: Generating Adversarial Text Against Real-world Applications](https://mlsanity.com/paper/1812.05271/) (2018)
- [Concrete Dropout](https://mlsanity.com/paper/1705.07832/) (2017)
- [Maxout Networks](https://mlsanity.com/paper/1302.4389/) (2013)
- [Certified Robustness to Adversarial Word Substitutions](https://mlsanity.com/paper/1909.00986/) (2019)
- [Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches](https://mlsanity.com/paper/1803.04386/) (2018)
- [Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programming](https://mlsanity.com/paper/1903.01287/) (2019)
- [Invertible generative models for inverse problems: mitigating representation error and dataset bias](https://mlsanity.com/paper/1905.11672/) (2019)
- [Achieving Verified Robustness to Symbol Substitutions via Interval Bound Propagation](https://mlsanity.com/paper/1909.01492/) (2019)
- [Imitation Attacks and Defenses for Black-box Machine Translation Systems](https://mlsanity.com/paper/2004.15015/) (2020)
- [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)
- [Sparse Adversarial Perturbations for Videos](https://mlsanity.com/paper/1803.02536/) (2018)
- [Learning to Discriminate Perturbations for Blocking Adversarial Attacks in Text Classification](https://mlsanity.com/paper/1909.03084/) (2019)
- [Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imaging](https://mlsanity.com/paper/2010.14462/) (2020)
- [Training verified learners with learned verifiers](https://mlsanity.com/paper/1805.10265/) (2018)
- [Robustness of Bayesian Neural Networks to Gradient-Based Attacks](https://mlsanity.com/paper/2002.04359/) (2020)
- [Composing Normalizing Flows for Inverse Problems](https://mlsanity.com/paper/2002.11743/) (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)
- [Model-Based Robust Deep Learning: Generalizing to Natural, Out-of-Distribution Data](https://mlsanity.com/paper/2005.10247/) (2020)
- [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)

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

- [Uncertainty Quantification in Inverse Models in Hydrology](https://mlsanity.com/paper/2310.02193/) (2023)

## Abstract (arXiv)

The astounding success of these methods has made it imperative to obtain more explainable and trustworthy estimates from these models. In hydrology, basin characteristics can be noisy or missing, impacting streamflow prediction. For solving inverse problems in such applications, ensuring explainability is pivotal for tackling issues relating to data bias and large search space. We propose a probabilistic inverse model framework that can reconstruct robust hydrology basin characteristics from dynamic input weather driver and streamflow response data. We address two aspects of building more explainable inverse models, uncertainty estimation and robustness. This can help improve the trust of water managers, handling of noisy data and reduce costs. We propose uncertainty based learning method that offers 6% improvement in R2 for streamflow prediction (forward modeling) from inverse model inferred basin characteristic estimates, 17% reduction in uncertainty (40% in presence of noise) and 4% higher coverage rate for basin characteristics.