# Causal Climate Emulation with Bayesian Filtering

arXiv: https://arxiv.org/abs/2506.09891 · HTML: https://mlsanity.com/paper/2506.09891/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 79 references that are in the map.
- First posted on arXiv 11 Jun 2025.

## Builds on (most cited first, 30 of 35)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [ClimaX: A foundation model for weather and climate](https://mlsanity.com/paper/2301.10343/) (2023)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020)
- [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere](https://mlsanity.com/paper/2306.03838/) (2023)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Forecasting Global Weather with Graph Neural Networks](https://mlsanity.com/paper/2202.07575/) (2022)
- [Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets](https://mlsanity.com/paper/2003.03685/) (2020)
- [Dynamical Variational Autoencoders: A Comprehensive Review](https://mlsanity.com/paper/2008.12595/) (2020)
- [High-recall causal discovery for autocorrelated time series with latent confounders](https://mlsanity.com/paper/2007.01884/) (2020)
- [ACE2: Accurately learning subseasonal to decadal atmospheric variability and forced responses](https://mlsanity.com/paper/2411.11268/) (2024)
- [NTS-NOTEARS: Learning Nonparametric DBNs With Prior Knowledge](https://mlsanity.com/paper/2109.04286/) (2021)
- [Challenges of learning multi-scale dynamics with AI weather models: Implications for stability and one solution](https://mlsanity.com/paper/2304.07029/) (2023)
- [LUCIE: A Lightweight Uncoupled ClImate Emulator with long-term stability and physical consistency for O(1000)-member ensembles](https://mlsanity.com/paper/2405.16297/) (2024)
- [Advancing Parsimonious Deep Learning Weather Prediction using the HEALPix Mesh](https://mlsanity.com/paper/2311.06253/) (2023)
- [Controlled Sparsity via Constrained Optimization or: How I Learned to Stop Tuning Penalties and Love Constraints](https://mlsanity.com/paper/2208.04425/) (2022)
- [Iterative Causal Discovery in the Possible Presence of Latent Confounders and Selection Bias](https://mlsanity.com/paper/2111.04095/) (2021)
- [Coupled Ocean-Atmosphere Dynamics in a Machine Learning Earth System Model](https://mlsanity.com/paper/2406.08632/) (2024)
- [Probabilistic Emulation of a Global Climate Model with Spherical DYffusion](https://mlsanity.com/paper/2406.14798/) (2024)
- [From Temporal to Contemporaneous Iterative Causal Discovery in the Presence of Latent Confounders](https://mlsanity.com/paper/2306.00624/) (2023)

## Built on by (most cited first, 5 of 5)

- [How Can Machine Learning Emulators Best Support Climate Science?](https://mlsanity.com/paper/2603.22320/) (2026)
- [Emulating the Forced Response of Climate Models with Generative Machine Learning](https://mlsanity.com/paper/2605.16929/) (2026)
- [Learning Hierarchical Causal Representations of the Effects of Forcings on Temperature in Climate Models](https://mlsanity.com/paper/2609.30995/) (2026)
- [Identifiability Guarantees for Drivers and Dynamics of Delayed Physical Systems](https://mlsanity.com/paper/2609.37944/) (2026)
- [Artificial intelligence pathways from weather to climate](https://mlsanity.com/paper/2610.09770/) (2026)

## Abstract (arXiv)

Traditional models of climate change use complex systems of coupled equations to simulate physical processes across the Earth system. These simulations are highly computationally expensive, limiting our predictions of climate change and analyses of its causes and effects. Machine learning has the potential to quickly emulate data from climate models, but current approaches are not able to incorporate physically-based causal relationships. Here, we develop an interpretable climate model emulator based on causal representation learning. We derive a novel approach including a Bayesian filter for stable long-term autoregressive emulation. We demonstrate that our emulator learns accurate climate dynamics, and we show the importance of each one of its components on a realistic synthetic dataset and data from two widely deployed climate models.