# Enhancing predictive skills in physically-consistent way: Physics Informed Machine Learning for Hydrological Processes

arXiv: https://arxiv.org/abs/2104.11009 · HTML: https://mlsanity.com/paper/2104.11009/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 95 references that are in the map.
- First posted on arXiv 22 Apr 2021.

## Builds on (most cited first, 12 of 12)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Explaining Explanations: An Overview of Interpretability of Machine Learning](https://mlsanity.com/paper/1806.00069/) (2018)
- [pymoo: Multi-objective Optimization in Python](https://mlsanity.com/paper/2002.04504/) (2020)
- [Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems](https://mlsanity.com/paper/2003.04919/) (2020)
- [A Theoretically Grounded Application of Dropout in Recurrent Neural Networks](https://mlsanity.com/paper/1512.05287/) (2015)
- [Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling](https://mlsanity.com/paper/1710.11431/) (2017)
- [Physics Guided RNNs for Modeling Dynamical Systems: A Case Study in Simulating Lake Temperature Profiles](https://mlsanity.com/paper/1810.13075/) (2018)
- [Physics-guided Convolutional Neural Network (PhyCNN) for Data-driven Seismic Response Modeling](https://mlsanity.com/paper/1909.08118/) (2019)
- [Enhancing streamflow forecast and extracting insights using long-short term memory networks with data integration at continental scales](https://mlsanity.com/paper/1912.08949/) (2019)
- [Physics Guided Machine Learning Methods for Hydrology](https://mlsanity.com/paper/2012.02854/) (2020)
- [Uncertainty Estimation with Deep Learning for Rainfall-Runoff Modelling](https://mlsanity.com/paper/2012.14295/) (2020)
- [Physics-guided Design and Learning of Neural Networks for Predicting Drag Force on Particle Suspensions in Moving Fluids](https://mlsanity.com/paper/1911.04240/) (2019)

## Built on by (most cited first, 6 of 6)

- [A Review of Physics-based Machine Learning in Civil Engineering](https://mlsanity.com/paper/2110.04600/) (2021)
- [Time Series Predictions in Unmonitored Sites: A Survey of Machine Learning Techniques in Water Resources](https://mlsanity.com/paper/2308.09766/) (2023)
- [Towards Interpretable Physical-Conceptual Catchment-Scale Hydrological Modeling using the Mass-Conserving-Perceptron](https://mlsanity.com/paper/2401.14521/) (2024)
- [SWAT Watershed Model Calibration using Deep Learning](https://mlsanity.com/paper/2110.03097/) (2021)
- [Identifying Trustworthiness Challenges in Deep Learning Models for Continental-Scale Water Quality Prediction](https://mlsanity.com/paper/2503.09947/) (2025)
- [HydroAgent: Formalizing Forecaster Expertise into Skill-Orchestrated Flood Forecasting Workflows](https://mlsanity.com/paper/2607.23983/) (2026)

## Abstract (arXiv)

Current modeling approaches for hydrological modeling often rely on either physics-based or data-science methods, including Machine Learning (ML) algorithms. While physics-based models tend to rigid structure resulting in unrealistic parameter values in certain instances, ML algorithms establish the input-output relationship while ignoring the constraints imposed by well-known physical processes. While there is a notion that the physics model enables better process understanding and ML algorithms exhibit better predictive skills, scientific knowledge that does not add to predictive ability may be deceptive. Hence, there is a need for a hybrid modeling approach to couple ML algorithms and physics-based models in a synergistic manner. Here we develop a Physics Informed Machine Learning (PIML) model that combines the process understanding of conceptual hydrological model with predictive abilities of state-of-the-art ML models. We apply the proposed model to predict the monthly time series of the target (streamflow) and intermediate variables (actual evapotranspiration) in the Narmada river basin in India. Our results show the capability of the PIML model to outperform a purely conceptual model (abcd model) and ML algorithms while ensuring the physical consistency in outputs validated through water balance analysis. The systematic approach for combining conceptual model structure with ML algorithms could be used to improve the predictive accuracy of crucial hydrological processes important for flood risk assessment.