# Physics-constrained deep learning postprocessing of temperature and humidity

arXiv: https://arxiv.org/abs/2212.04487 · HTML: https://mlsanity.com/paper/2212.04487/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 35 references that are in the map.
- First posted on arXiv 7 Dec 2022.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Tune: A Research Platform for Distributed Model Selection and Training](https://mlsanity.com/paper/1807.05118/) (2018)
- [Multi-Task Learning with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2009.09796/) (2020)
- [Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems](https://mlsanity.com/paper/2003.04919/) (2020)
- [Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling](https://mlsanity.com/paper/1710.11431/) (2017)
- [Neural networks for post-processing ensemble weather forecasts](https://mlsanity.com/paper/1805.09091/) (2018)
- [Deep Learning for Post-Processing Ensemble Weather Forecasts](https://mlsanity.com/paper/2005.08748/) (2020)
- [Machine learning methods for postprocessing ensemble forecasts of wind gusts: A systematic comparison](https://mlsanity.com/paper/2106.09512/) (2021)
- [Towards Physically-consistent, Data-driven Models of Convection](https://mlsanity.com/paper/2002.08525/) (2020)
- [CIRA Guide to Custom Loss Functions for Neural Networks in Environmental Sciences -- Version 1](https://mlsanity.com/paper/2106.09757/) (2021)

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

- [Shaping the Wind: Nested Potentials for Kinematically Admissible Urban Wind Prediction](https://mlsanity.com/paper/2610.07033/) (2026)

## Abstract (arXiv)

Weather forecasting centers currently rely on statistical postprocessing methods to minimize forecast error. This improves skill but can lead to predictions that violate physical principles or disregard dependencies between variables, which can be problematic for downstream applications and for the trustworthiness of postprocessing models, especially when they are based on new machine learning approaches. Building on recent advances in physics-informed machine learning, we propose to achieve physical consistency in deep learning-based postprocessing models by integrating meteorological expertise in the form of analytic equations. Applied to the post-processing of surface weather in Switzerland, we find that constraining a neural network to enforce thermodynamic state equations yields physically-consistent predictions of temperature and humidity without compromising performance. Our approach is especially advantageous when data is scarce, and our findings suggest that incorporating domain expertise into postprocessing models allows to optimize weather forecast information while satisfying application-specific requirements.