# A non-intrusive machine learning framework for debiasing long-time coarse resolution climate simulations and quantifying rare events statistics

arXiv: https://arxiv.org/abs/2402.18484 · HTML: https://mlsanity.com/paper/2402.18484/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 86 references that are in the map.
- First posted on arXiv 28 Feb 2024.

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

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers](https://mlsanity.com/paper/2111.13587/) (2021)
- [Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere](https://mlsanity.com/paper/2306.03838/) (2023)
- [Deep learning to represent sub-grid processes in climate models](https://mlsanity.com/paper/1806.04731/) (2018)
- [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018)
- [Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High-Resolution Simulations](https://mlsanity.com/paper/1709.00037/) (2017)
- [Machine Learning for Prediction with Missing Dynamics](https://mlsanity.com/paper/1910.05861/) (2019)
- [Learning bias corrections for climate models using deep neural operators](https://mlsanity.com/paper/2302.03173/) (2023)
- [A Multi-Scale Deep Learning Framework for Projecting Weather Extremes](https://mlsanity.com/paper/2210.12137/) (2022)
- [Error Bounds of the Invariant Statistics in Machine Learning of Ergodic Ito Diffusions](https://mlsanity.com/paper/2105.10102/) (2021)
- [Stabilizing Machine Learning Prediction of Dynamics: Noise and Noise-inspired Regularization](https://mlsanity.com/paper/2211.05262/) (2022)

## Built on by (most cited first, 9 of 9)

- [Probabilistic Emulation of a Global Climate Model with Spherical DYffusion](https://mlsanity.com/paper/2406.14798/) (2024)
- [A probabilistic framework for learning non-intrusive corrections to long-time climate simulations from short-time training data](https://mlsanity.com/paper/2408.02688/) (2024)
- [GEN2: A Generative Prediction-Correction Framework for Long-time Emulations of Spatially-Resolved Climate Extremes](https://mlsanity.com/paper/2508.15196/) (2025)
- [Retrofitting Earth System Models with Cadence-Limited Neural Operator Updates](https://mlsanity.com/paper/2512.03309/) (2025)
- [Toward generative machine learning for boosting ensembles of climate simulations](https://mlsanity.com/paper/2602.06287/) (2026)
- [Mixing Artificial and Natural Intelligence: From Statistical Mechanics to AI and Back to Turbulence](https://mlsanity.com/paper/2403.17993/) (2024)
- [Climate Model Tuning with Online Synchronization-Based Parameter Estimation](https://mlsanity.com/paper/2510.06180/) (2025)
- [DySCo: Dynamically consistent data-driven downscaling of extremes in climate projections](https://mlsanity.com/paper/2608.21998/) (2026)
- [Mechanism-Aware Ensemble Conditioning for Data-Limited Emulation of Extreme Events](https://mlsanity.com/paper/2609.30746/) (2026)

## Abstract (arXiv)

Due to the rapidly changing climate, the frequency and severity of extreme weather is expected to increase over the coming decades. As fully-resolved climate simulations remain computationally intractable, policy makers must rely on coarse-models to quantify risk for extremes. However, coarse models suffer from inherent bias due to the ignored "sub-grid" scales. We propose a framework to non-intrusively debias coarse-resolution climate predictions using neural-network (NN) correction operators. Previous efforts have attempted to train such operators using loss functions that match statistics. However, this approach falls short with events that have longer return period than that of the training data, since the reference statistics have not converged. Here, the scope is to formulate a learning method that allows for correction of dynamics and quantification of extreme events with longer return period than the training data. The key obstacle is the chaotic nature of the underlying dynamics. To overcome this challenge, we introduce a dynamical systems approach where the correction operator is trained using reference data and a coarse model simulation nudged towards that reference. The method is demonstrated on debiasing an under-resolved quasi-geostrophic model and the Energy Exascale Earth System Model (E3SM). For the former, our method enables the quantification of events that have return period two orders longer than the training data. For the latter, when trained on 8 years of ERA5 data, our approach is able to correct the coarse E3SM output to closely reflect the 36-year ERA5 statistics for all prognostic variables and significantly reduce their spatial biases.