# Physically Constrained Generative Adversarial Networks for Improving Precipitation Fields from Earth System Models

arXiv: https://arxiv.org/abs/2209.07568 · HTML: https://mlsanity.com/paper/2209.07568/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 78 references that are in the map.
- First posted on arXiv 25 Aug 2022.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [CyCADA: Cycle-Consistent Adversarial Domain Adaptation](https://mlsanity.com/paper/1711.03213/) (2017)
- [Skillful Precipitation Nowcasting using Deep Generative Models of Radar](https://mlsanity.com/paper/2104.00954/) (2021)
- [DualGAN: Unsupervised Dual Learning for Image-to-Image Translation](https://mlsanity.com/paper/1704.02510/) (2017)
- [Interpretable machine learning: definitions, methods, and applications](https://mlsanity.com/paper/1901.04592/) (2019)
- [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020)
- [Neural networks for post-processing ensemble weather forecasts](https://mlsanity.com/paper/1805.09091/) (2018)
- [A Generative Deep Learning Approach to Stochastic Downscaling of Precipitation Forecasts](https://mlsanity.com/paper/2204.02028/) (2022)
- [Deep Learning for Post-Processing Ensemble Weather Forecasts](https://mlsanity.com/paper/2005.08748/) (2020)
- [Machine Learning for Stochastic Parameterization: Generative Adversarial Networks in the Lorenz '96 Model](https://mlsanity.com/paper/1909.04711/) (2019)
- [Physically Interpretable Neural Networks for the Geosciences: Applications to Earth System Variability](https://mlsanity.com/paper/1912.01752/) (2019)
- [Increasing the accuracy and resolution of precipitation forecasts using deep generative models](https://mlsanity.com/paper/2203.12297/) (2022)

## Built on by (most cited first, 29 of 29)

- [Fast, Scale-Adaptive, and Uncertainty-Aware Downscaling of Earth System Model Fields with Generative Machine Learning](https://mlsanity.com/paper/2403.02774/) (2024)
- [Generative machine learning methods for multivariate ensemble post-processing](https://mlsanity.com/paper/2211.01345/) (2022)
- [Conditional diffusion models for downscaling and bias correction of Earth system model precipitation](https://mlsanity.com/paper/2404.14416/) (2024)
- [Machine learning emulation of precipitation from km-scale UK regional climate simulations using a diffusion model](https://mlsanity.com/paper/2407.14158/) (2024)
- [WeatherGNN: Exploiting Meteo- and Spatial-Dependencies for Local Numerical Weather Prediction Bias-Correction](https://mlsanity.com/paper/2310.05517/) (2023)
- [When Geoscience Meets Foundation Models: Towards General Geoscience Artificial Intelligence System](https://mlsanity.com/paper/2309.06799/) (2023)
- [MambaDS: Near-Surface Meteorological Field Downscaling with Topography Constrained Selective State Space Modeling](https://mlsanity.com/paper/2408.10854/) (2024)
- [A Generative Framework for Probabilistic, Spatiotemporally Coherent Downscaling of Climate Simulation](https://mlsanity.com/paper/2412.15361/) (2024)
- [Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology](https://mlsanity.com/paper/2310.05227/) (2023)
- [Global spatio-temporal downscaling of ERA5 precipitation through generative AI](https://mlsanity.com/paper/2411.16098/) (2024)
- [Generative assimilation and prediction for weather and climate](https://mlsanity.com/paper/2503.03038/) (2025)
- [Observation-Guided Meteorological Field Downscaling at Station Scale: A Benchmark and a New Method](https://mlsanity.com/paper/2401.11960/) (2024)
- [Deep learning for bias-correcting CMIP6-class Earth system models](https://mlsanity.com/paper/2301.01253/) (2022)
- [Multi-variable Hard Physical Constraints for Climate Model Downscaling](https://mlsanity.com/paper/2308.01868/) (2023)
- [Improving Global Weather and Ocean Wave Forecast with Large Artificial Intelligence Models](https://mlsanity.com/paper/2401.16669/) (2024)
- [Reconstructing Historical Climate Fields With Deep Learning](https://mlsanity.com/paper/2311.18348/) (2023)
- [Differential-Integral Neural Operator for Long-Term Turbulence Forecasting](https://mlsanity.com/paper/2509.21196/) (2025)
- [Logic Tensor Network-Enhanced Generative Adversarial Network](https://mlsanity.com/paper/2601.03839/) (2026)
- [Exploring Geometric Deep Learning For Precipitation Nowcasting](https://mlsanity.com/paper/2309.05828/) (2023)
- [Generating realistic global precipitation fields from modelled atmospheric circulation](https://mlsanity.com/paper/2504.00307/) (2025)
- [PnP-Corrector: A Universal Correction Framework for Coupled Spatiotemporal Forecasting](https://mlsanity.com/paper/2605.08935/) (2026)
- [Towards replacing precipitation ensemble predictions systems using machine learning](https://mlsanity.com/paper/2304.10251/) (2023)
- [Applications of Explainable artificial intelligence in Earth system science](https://mlsanity.com/paper/2406.11882/) (2024)
- [Diffusion-Based Joint Temperature and Precipitation Emulation of Earth System Models](https://mlsanity.com/paper/2404.08797/) (2024)
- [Physics-Guided Multimodal Transformers are the Necessary Foundation for the Next Generation of Meteorological Science](https://mlsanity.com/paper/2504.14174/) (2025)
- [Data-driven solar forecasting enables near-optimal economic decisions](https://mlsanity.com/paper/2509.06925/) (2025)
- [Generate in the Chart, Not on the Boundary: Function-Symbol Grounding for Hard Constraints in LTN-GANs](https://mlsanity.com/paper/2608.21605/) (2026)
- [StatD2GAN: When Calibration Masks Generator Quality in Held-Out Evaluation of Synthetic Weather Sequences](https://mlsanity.com/paper/2609.33761/) (2026)
- [Generalizable Neural Downscaling of Earth System Model Wind Fields via Continuous Dynamics Modeling](https://mlsanity.com/paper/2610.03757/) (2026)

## Abstract (arXiv)

Precipitation results from complex processes across many scales, making its accurate simulation in Earth system models (ESMs) challenging. Existing post-processing methods can improve ESM simulations locally, but cannot correct errors in modelled spatial patterns. Here we propose a framework based on physically constrained generative adversarial networks (GANs) to improve local distributions and spatial structure simultaneously. We apply our approach to the computationally efficient ESM CM2Mc-LPJmL. Our method outperforms existing ones in correcting local distributions, and leads to strongly improved spatial patterns especially regarding the intermittency of daily precipitation. Notably, a double-peaked Intertropical Convergence Zone, a common problem in ESMs, is removed. Enforcing a physical constraint to preserve global precipitation sums, the GAN can generalize to future climate scenarios unseen during training. Feature attribution shows that the GAN identifies regions where the ESM exhibits strong biases. Our method constitutes a general framework for correcting ESM variables and enables realistic simulations at a fraction of the computational costs.