# A probabilistic framework for learning non-intrusive corrections to long-time climate simulations from short-time training data arXiv: https://arxiv.org/abs/2408.02688 ยท HTML: https://mlsanity.com/paper/2408.02688/ ## Key facts - Cited by 5 papers in the map (data through 14 Oct 2026). - Builds on 31 of its 113 references that are in the map. - First posted on arXiv 2 Aug 2024. ## Builds on (most cited first, 30 of 31) - [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014) - [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014) - [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020) - [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014) - [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022) - [Speech Recognition with Deep Recurrent Neural Networks](https://mlsanity.com/paper/1303.5778/) (2013) - [Generating Sequences With Recurrent Neural Networks](https://mlsanity.com/paper/1308.0850/) (2013) - [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021) - [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015) - [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022) - [Generalized Zero- and Few-Shot Learning via Aligned Variational Autoencoders](https://mlsanity.com/paper/1812.01784/) (2018) - [Deep learning to represent sub-grid processes in climate models](https://mlsanity.com/paper/1806.04731/) (2018) - [Sequential Neural Models with Stochastic Layers](https://mlsanity.com/paper/1605.07571/) (2016) - [DeepSD: Generating High Resolution Climate Change Projections through Single Image Super-Resolution](https://mlsanity.com/paper/1703.03126/) (2017) - [Learning Stochastic Recurrent Networks](https://mlsanity.com/paper/1411.7610/) (2014) - [ACE: A fast, skillful learned global atmospheric model for climate prediction](https://mlsanity.com/paper/2310.02074/) (2023) - [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) - [Learning to correct spectral methods for simulating turbulent flows](https://mlsanity.com/paper/2207.00556/) (2022) - [Training neural operators to preserve invariant measures of chaotic attractors](https://mlsanity.com/paper/2306.01187/) (2023) - [Debias Coarsely, Sample Conditionally: Statistical Downscaling through Optimal Transport and Probabilistic Diffusion Models](https://mlsanity.com/paper/2305.15618/) (2023) - [Deep State Space Models for Nonlinear System Identification](https://mlsanity.com/paper/2003.14162/) (2020) - [DySLIM: Dynamics Stable Learning by Invariant Measure for Chaotic Systems](https://mlsanity.com/paper/2402.04467/) (2024) - [Data Augmentation in High Dimensional Low Sample Size Setting Using a Geometry-Based Variational Autoencoder](https://mlsanity.com/paper/2105.00026/) (2021) - [Unpaired Downscaling of Fluid Flows with Diffusion Bridges](https://mlsanity.com/paper/2305.01822/) (2023) - [Neural Ideal Large Eddy Simulation: Modeling Turbulence with Neural Stochastic Differential Equations](https://mlsanity.com/paper/2306.01174/) (2023) - [Learning bias corrections for climate models using deep neural operators](https://mlsanity.com/paper/2302.03173/) (2023) - [A non-intrusive machine learning framework for debiasing long-time coarse resolution climate simulations and quantifying rare events statistics](https://mlsanity.com/paper/2402.18484/) (2024) - [A Multi-Scale Deep Learning Framework for Projecting Weather Extremes](https://mlsanity.com/paper/2210.12137/) (2022) - [Constraining Chaos: Enforcing dynamical invariants in the training of recurrent neural networks](https://mlsanity.com/paper/2304.12865/) (2023) - [Error Bounds of the Invariant Statistics in Machine Learning of Ergodic Ito Diffusions](https://mlsanity.com/paper/2105.10102/) (2021) ## Built on by (most cited first, 5 of 5) - [Dynamical-generative downscaling of climate model ensembles](https://mlsanity.com/paper/2410.01776/) (2024) - [Project and Generate: Divergence-Free Neural Operators for Incompressible Flows](https://mlsanity.com/paper/2603.24500/) (2026) - [GEN2: A Generative Prediction-Correction Framework for Long-time Emulations of Spatially-Resolved Climate Extremes](https://mlsanity.com/paper/2508.15196/) (2025) - [Toward generative machine learning for boosting ensembles of climate simulations](https://mlsanity.com/paper/2602.06287/) (2026) - [Mechanism-Aware Ensemble Conditioning for Data-Limited Emulation of Extreme Events](https://mlsanity.com/paper/2609.30746/) (2026) ## Abstract (arXiv) Chaotic systems, such as turbulent flows, are ubiquitous in science and engineering. However, their study remains a challenge due to the large range scales, and the strong interaction with other, often not fully understood, physics. As a consequence, the spatiotemporal resolution required for accurate simulation of these systems is typically computationally infeasible, particularly for applications of long-term risk assessment, such as the quantification of extreme weather risk due to climate change. While data-driven modeling offers some promise of alleviating these obstacles, the scarcity of high-quality simulations results in limited available data to train such models, which is often compounded by the lack of stability for long-horizon simulations. As such, the computational, algorithmic, and data restrictions generally imply that the probability of rare extreme events is not accurately captured. In this work we present a general strategy for training neural network models to non-intrusively correct under-resolved long-time simulations of chaotic systems. The approach is based on training a post-processing correction operator on under-resolved simulations nudged towards a high-fidelity reference. This enables us to learn the dynamics of the underlying system directly, which allows us to use very little training data, even when the statistics thereof are far from converged. Additionally, through the use of probabilistic network architectures we are able to leverage the uncertainty due to the limited training data to further improve extrapolation capabilities. We apply our framework to severely under-resolved simulations of quasi-geostrophic flow and demonstrate its ability to accurately predict the anisotropic statistics over time horizons more than 30 times longer than the data seen in training.