# Probing forced responses and causality in data-driven climate emulators: conceptual limitations and the role of reduced-order models

arXiv: https://arxiv.org/abs/2506.22552 · HTML: https://mlsanity.com/paper/2506.22552/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 160 references that are in the map.
- First posted on arXiv 27 Jun 2025.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [Probabilistic Forecasting with Stochastic Interpolants and F"ollmer Processes](https://mlsanity.com/paper/2403.13724/) (2024)
- [Skillful joint probabilistic weather forecasting from marginals](https://mlsanity.com/paper/2506.10772/) (2025)
- [Deep Bayesian Inversion](https://mlsanity.com/paper/1811.05910/) (2018)
- [ACE: A fast, skillful learned global atmospheric model for climate prediction](https://mlsanity.com/paper/2310.02074/) (2023)
- [ACE2: Accurately learning subseasonal to decadal atmospheric variability and forced responses](https://mlsanity.com/paper/2411.11268/) (2024)
- [Samudra: An AI Global Ocean Emulator for Climate](https://mlsanity.com/paper/2412.03795/) (2024)
- [Can AI weather models predict out-of-distribution gray swan tropical cyclones?](https://mlsanity.com/paper/2410.14932/) (2024)
- [OceanNet: A principled neural operator-based digital twin for regional oceans](https://mlsanity.com/paper/2310.00813/) (2023)
- [Thermalizer: Stable autoregressive neural emulation of spatiotemporal chaos](https://mlsanity.com/paper/2503.18731/) (2025)
- [The impact of internal variability on benchmarking deep learning climate emulators](https://mlsanity.com/paper/2408.05288/) (2024)
- [Hierarchical Implicit Neural Emulators](https://mlsanity.com/paper/2506.04528/) (2025)
- [Physics-aware generative models for turbulent fluid flows through energy-consistent stochastic interpolants](https://mlsanity.com/paper/2504.05852/) (2025)
- [Predicting Forced Responses of Probability Distributions via the Fluctuation-Dissipation Theorem and Generative Modeling](https://mlsanity.com/paper/2504.13333/) (2025)
- [Minimum Reduced-Order Models via Causal Inference](https://mlsanity.com/paper/2407.00271/) (2024)

## Built on by (most cited first, 6 of 6)

- [Project and Generate: Divergence-Free Neural Operators for Incompressible Flows](https://mlsanity.com/paper/2603.24500/) (2026)
- [FloeNet: A mass-conserving global sea ice emulator that generalizes across climates](https://mlsanity.com/paper/2603.12449/) (2026)
- [AI-boosted rare event sampling to characterize extreme weather](https://mlsanity.com/paper/2510.27066/) (2025)
- [Reduced-Order Modeling of Cyclo-Stationary Time Series Using Score-Based Generative Methods](https://mlsanity.com/paper/2508.19448/) (2025)
- [Conditional Score-Based Modeling of Effective Langevin Dynamics](https://mlsanity.com/paper/2604.23952/) (2026)
- [Missing the Butterfly and Predicting the Past: Features or Bugs of Accurate AI Weather Models?](https://mlsanity.com/paper/2608.25835/) (2026)

## Abstract (arXiv)

A central challenge in climate science and applied mathematics is developing data-driven models of multiscale systems that capture both stationary statistics and responses to external perturbations. Current neural climate emulators aim to resolve the atmosphere-ocean system in all its complexity but often struggle to reproduce forced responses, limiting their use in causal studies such as Green's function experiments. To explore the origin of these limitations, we first examine a simplified dynamical system that retains key features of climate variability. We interpret the results through linear response theory, providing a rigorous framework to evaluate neural models beyond stationary statistics and to probe causal mechanisms. We argue that the ability of emulators of multiscale systems to reproduce perturbed statistics depends critically on (i) the choice of an appropriate coarse-grained representation and (ii) careful parameterizations of unresolved processes. These insights highlight reduced-order models, tailored to specific goals, processes, and scales, as valuable alternatives to general-purpose emulators. We next consider a real-world application by developing a neural model to investigate the joint variability of the surface temperature field and radiative fluxes. The model infers a multiplicative noise process directly from data, largely reproduces the system's probability distribution, and enables causal studies through forced responses. We discuss its limitations and outline directions for future work. Overall, these results expose key challenges in data-driven modeling of multiscale physical systems and underscore the value of coarse-grained, stochastic approaches, with response theory providing a principled framework to guide model design and enhance causal understanding.