# Optimal scenario design for climate emulation

arXiv: https://arxiv.org/abs/2606.19302 · HTML: https://mlsanity.com/paper/2606.19302/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 77 references that are in the map.
- First posted on arXiv 17 Jun 2026.

## Builds on (most cited first, 18 of 18)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Dataset Distillation by Matching Training Trajectories](https://mlsanity.com/paper/2203.11932/) (2022)
- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [Dataset Distillation with Infinitely Wide Convolutional Networks](https://mlsanity.com/paper/2107.13034/) (2021)
- [An Exponential Learning Rate Schedule for Deep Learning](https://mlsanity.com/paper/1910.07454/) (2019)
- [An Improved Analysis of Stochastic Gradient Descent with Momentum](https://mlsanity.com/paper/2007.07989/) (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)
- [DiffESM: Conditional Emulation of Temperature and Precipitation in Earth System Models with 3D Diffusion Models](https://mlsanity.com/paper/2409.11601/) (2024)
- [The impact of internal variability on benchmarking deep learning climate emulators](https://mlsanity.com/paper/2408.05288/) (2024)
- [Enhancing Physics-Informed Neural Networks Through Feature Engineering](https://mlsanity.com/paper/2502.07209/) (2025)
- [Physics-guided Data Augmentation for Learning the Solution Operator of Linear Differential Equations](https://mlsanity.com/paper/2212.04100/) (2022)
- [FaIRGP: A Bayesian Energy Balance Model for Surface Temperatures Emulation](https://mlsanity.com/paper/2307.10052/) (2023)
- [Score-based generative emulation of impact-relevant Earth system model outputs](https://mlsanity.com/paper/2510.04358/) (2025)

## Built on by (most cited first, 1 of 1)

- [Optimizing Geoengineering Interventions Using Differentiable Climate Models](https://mlsanity.com/paper/2609.12528/) (2026)

## Abstract (arXiv)

As deep learning for physical systems continues to grow in popularity, efforts to improve generalizability have primarily focused on designing architectures that embed physical constraints. However, for machine-learning surrogate climate models (emulators), we show that the low structural diversity in existing scenarios commonly used to generate training data places a ceiling on predictive skill. Here, we examine whether training datasets themselves can be optimized to improve generalization. We introduce a method to create datasets that produce emulators capable of generalizing to new, structurally different scenarios absent from the training data. We use a differentiable Simple Climate Model (SCM) to calculate the sensitivity of emulator loss to perturbations in the training data, iteratively updating the training data to maximize emulator skill. For an SCM, training on one scenario optimized in this fashion outperforms an emulator trained on six standard ScenarioMIP pathways. We achieve this higher predictive skill despite training on a smaller dataset, finding that our emulator successfully isolates distinct physical behaviors of different climate forcing agents (e.g., greenhouse gases vs. aerosols) without single-forcing runs. We then demonstrate that scenarios optimized using an SCM, when used to drive an intermediate-complexity climate model, produce a training dataset that yields a more skillful emulator than training on ScenarioMIP outputs. Our results suggest that, in the compute-constrained environment of running full-scale climate models, generating a small number of dynamically rich scenarios provides greater marginal value for emulation and characterizing system responses than expanding the suite of traditional emissions pathways.