# FaIRGP: A Bayesian Energy Balance Model for Surface Temperatures Emulation

arXiv: https://arxiv.org/abs/2307.10052 · HTML: https://mlsanity.com/paper/2307.10052/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 94 references that are in the map.
- First posted on arXiv 14 Jul 2023.

## Builds on (most cited first, 6 of 6)

- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Exact Gaussian Processes on a Million Data Points](https://mlsanity.com/paper/1903.08114/) (2019)
- [On Sparse variational methods and the Kullback-Leibler divergence between stochastic processes](https://mlsanity.com/paper/1504.07027/) (2015)
- [Hyperparameter Learning via Distributional Transfer](https://mlsanity.com/paper/1810.06305/) (2018)

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

- [The impact of internal variability on benchmarking deep learning climate emulators](https://mlsanity.com/paper/2408.05288/) (2024)
- [Spatiotemporal Pyramid Flow Matching for Climate Emulation](https://mlsanity.com/paper/2512.02268/) (2025)
- [Score-based generative emulation of impact-relevant Earth system model outputs](https://mlsanity.com/paper/2510.04358/) (2025)
- [Optimal scenario design for climate emulation](https://mlsanity.com/paper/2606.19302/) (2026)
- [Toward Artificial Intelligence Enabled Earth System Coupling](https://mlsanity.com/paper/2604.03289/) (2026)

## Abstract (arXiv)

Emulators, or reduced complexity climate models, are surrogate Earth system models that produce projections of key climate quantities with minimal computational resources. Using time-series modelling or more advanced machine learning techniques, data-driven emulators have emerged as a promising avenue of research, producing spatially resolved climate responses that are visually indistinguishable from state-of-the-art Earth system models. Yet, their lack of physical interpretability limits their wider adoption. In this work, we introduce FaIRGP, a data-driven emulator that satisfies the physical temperature response equations of an energy balance model. The result is an emulator that textit(i) enjoys the flexibility of statistical machine learning models and can learn from data, and textit(ii) has a robust physical grounding with interpretable parameters that can be used to make inference about the climate system. Further, our Bayesian approach allows a principled and mathematically tractable uncertainty quantification. Our model demonstrates skillful emulation of global mean surface temperature and spatial surface temperatures across realistic future scenarios. Its ability to learn from data allows it to outperform energy balance models, while its robust physical foundation safeguards against the pitfalls of purely data-driven models. We also illustrate how FaIRGP can be used to obtain estimates of top-of-atmosphere radiative forcing and discuss the benefits of its mathematical tractability for applications such as detection and attribution or precipitation emulation. We hope that this work will contribute to widening the adoption of data-driven methods in climate emulation.