# Multi-fidelity climate model parameterization for better generalization and extrapolation

arXiv: https://arxiv.org/abs/2309.10231 · HTML: https://mlsanity.com/paper/2309.10231/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 85 references that are in the map.
- First posted on arXiv 19 Sep 2023.

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

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [Scale-MAE: A Scale-Aware Masked Autoencoder for Multiscale Geospatial Representation Learning](https://mlsanity.com/paper/2212.14532/) (2022)
- [Randomized Prior Functions for Deep Reinforcement Learning](https://mlsanity.com/paper/1806.03335/) (2018)
- [Deep Bayesian Bandits Showdown: An Empirical Comparison of Bayesian Deep Networks for Thompson Sampling](https://mlsanity.com/paper/1802.09127/) (2018)
- [Deep learning to represent sub-grid processes in climate models](https://mlsanity.com/paper/1806.04731/) (2018)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [Multi-fidelity Bayesian Neural Networks: Algorithms and Applications](https://mlsanity.com/paper/2012.13294/) (2020)
- [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)
- [Scalable Uncertainty Quantification for Deep Operator Networks using Randomized Priors](https://mlsanity.com/paper/2203.03048/) (2022)
- [A posteriori learning for quasi-geostrophic turbulence parametrization](https://mlsanity.com/paper/2204.03911/) (2022)
- [Bayesian differential programming for robust systems identification under uncertainty](https://mlsanity.com/paper/2004.06843/) (2020)
- [A Fortran-Keras Deep Learning Bridge for Scientific Computing](https://mlsanity.com/paper/2004.10652/) (2020)
- [Bridging observation, theory and numerical simulation of the ocean using Machine Learning](https://mlsanity.com/paper/2104.12506/) (2021)
- [Multi-fidelity Hierarchical Neural Processes](https://mlsanity.com/paper/2206.04872/) (2022)
- [Machine-learned climate model corrections from a global storm-resolving model](https://mlsanity.com/paper/2211.11820/) (2022)
- [Scalable Bayesian optimization with high-dimensional outputs using randomized prior networks](https://mlsanity.com/paper/2302.07260/) (2023)

## Built on by (most cited first, 4 of 4)

- [Joint Parameter and Parameterization Inference with Uncertainty Quantification through Differentiable Programming](https://mlsanity.com/paper/2403.02215/) (2024)
- [Navigating the Noise: Bringing Clarity to ML Parameterization Design with O(100) Ensembles](https://mlsanity.com/paper/2309.16177/) (2023)
- [Crowdsourcing the Frontier: Advancing Hybrid Physics-ML Climate Simulation via a 50,000 Kaggle Competition](https://mlsanity.com/paper/2511.20963/) (2025)
- [No Epoch Like the Present: Robust Climate Emulation Requires Out-of-Distribution Generalisation](https://mlsanity.com/paper/2605.22248/) (2026)

## Abstract (arXiv)

Machine-learning-based parameterizations (i.e. representation of sub-grid processes) of global climate models or turbulent simulations have recently been proposed as a powerful alternative to physical, but empirical, representations, offering a lower computational cost and higher accuracy. Yet, those approaches still suffer from a lack of generalization and extrapolation beyond the training data, which is however critical to projecting climate change or unobserved regimes of turbulence. Here we show that a multi-fidelity approach, which integrates datasets of different accuracy and abundance, can provide the best of both worlds: the capacity to extrapolate leveraging the physically-based parameterization and a higher accuracy using the machine-learning-based parameterizations. In an application to climate modeling, the multi-fidelity framework yields more accurate climate projections without requiring major increase in computational resources. Our multi-fidelity randomized prior networks (MF-RPNs) combine physical parameterization data as low-fidelity and storm-resolving historical run's data as high-fidelity. To extrapolate beyond the training data, the MF-RPNs are tested on high-fidelity warming scenarios, +4K, data. We show the MF-RPN's capacity to return much more skillful predictions compared to either low- or high-fidelity (historical data) simulations trained only on one regime while providing trustworthy uncertainty quantification across a wide range of scenarios. Our approach paves the way for the use of machine-learning based methods that can optimally leverage historical observations or high-fidelity simulations and extrapolate to unseen regimes such as climate change.