# Towards Physically-consistent, Data-driven Models of Convection

arXiv: https://arxiv.org/abs/2002.08525 · HTML: https://mlsanity.com/paper/2002.08525/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2020.

## Built on by (most cited first, 13 of 13)

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- [Constraining Chaos: Enforcing dynamical invariants in the training of recurrent neural networks](https://mlsanity.com/paper/2304.12865/) (2023)
- [Deep Learning Based Cloud Cover Parameterization for ICON](https://mlsanity.com/paper/2112.11317/) (2021)
- [Using Probabilistic Machine Learning to Better Model Temporal Patterns in Parameterizations: a case study with the Lorenz 96 model](https://mlsanity.com/paper/2203.14814/) (2022)
- [Emulating Aerosol Microphysics with Machine Learning](https://mlsanity.com/paper/2109.10593/) (2021)
- [Inductive biases in deep learning models for weather prediction](https://mlsanity.com/paper/2304.04664/) (2023)
- [Online Test of a Neural Network Deep Convection Parameterization in ARP-GEM1](https://mlsanity.com/paper/2410.21920/) (2024)
- [Physics-constrained deep learning postprocessing of temperature and humidity](https://mlsanity.com/paper/2212.04487/) (2022)
- [Towards Physically Consistent Deep Learning For Climate Model Parameterizations](https://mlsanity.com/paper/2406.03920/) (2024)
- [No Epoch Like the Present: Robust Climate Emulation Requires Out-of-Distribution Generalisation](https://mlsanity.com/paper/2605.22248/) (2026)

## Abstract (arXiv)

Data-driven algorithms, in particular neural networks, can emulate the effect of sub-grid scale processes in coarse-resolution climate models if trained on high-resolution climate simulations. However, they may violate key physical constraints and lack the ability to generalize outside of their training set. Here, we show that physical constraints can be enforced in neural networks, either approximately by adapting the loss function or to within machine precision by adapting the architecture. As these physical constraints are insufficient to guarantee generalizability, we additionally propose to physically rescale the training and validation data to improve the ability of neural networks to generalize to unseen climates.