# Streamflow Prediction with Uncertainty Quantification for Water Management: A Constrained Reasoning and Learning Approach

arXiv: https://arxiv.org/abs/2406.00133 · HTML: https://mlsanity.com/paper/2406.00133/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 33 references that are in the map.
- First posted on arXiv 31 May 2024.

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

- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling](https://mlsanity.com/paper/1710.11431/) (2017)
- [Semantic Probabilistic Layers for Neuro-Symbolic Learning](https://mlsanity.com/paper/2206.00426/) (2022)
- [Physics-Guided Machine Learning for Scientific Discovery: An Application in Simulating Lake Temperature Profiles](https://mlsanity.com/paper/2001.11086/) (2020)
- [Physics Guided RNNs for Modeling Dynamical Systems: A Case Study in Simulating Lake Temperature Profiles](https://mlsanity.com/paper/1810.13075/) (2018)
- [Neuro-Symbolic Artificial Intelligence: Current Trends](https://mlsanity.com/paper/2105.05330/) (2021)
- [Understanding the role of importance weighting for deep learning](https://mlsanity.com/paper/2103.15209/) (2021)
- [MC-LSTM: Mass-Conserving LSTM](https://mlsanity.com/paper/2101.05186/) (2021)
- [Short-term Hourly Streamflow Prediction with Graph Convolutional GRU Networks](https://mlsanity.com/paper/2107.07039/) (2021)

## Abstract (arXiv)

Predicting the spatiotemporal variation in streamflow along with uncertainty quantification enables decision-making for sustainable management of scarce water resources. Process-based hydrological models (aka physics-based models) are based on physical laws, but using simplifying assumptions which can lead to poor accuracy. Data-driven approaches offer a powerful alternative, but they require large amount of training data and tend to produce predictions that are inconsistent with physical laws. This paper studies a constrained reasoning and learning (CRL) approach where physical laws represented as logical constraints are integrated as a layer in the deep neural network. To address small data setting, we develop a theoretically-grounded training approach to improve the generalization accuracy of deep models. For uncertainty quantification, we combine the synergistic strengths of Gaussian processes (GPs) and deep temporal models (i.e., deep models for time-series forecasting) by passing the learned latent representation as input to a standard distance-based kernel. Experiments on multiple real-world datasets demonstrate the effectiveness of both CRL and GP with deep kernel approaches over strong baseline methods.