# On the importance of learning non-local dynamics for stable data-driven climate modeling: A 1D gravity wave-QBO testbed

arXiv: https://arxiv.org/abs/2407.05224 · HTML: https://mlsanity.com/paper/2407.05224/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 68 references that are in the map.
- First posted on arXiv 7 Jul 2024.

## Builds on (most cited first, 13 of 13)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Understanding the Effective Receptive Field in Deep Convolutional Neural Networks](https://mlsanity.com/paper/1701.04128/) (2017)
- [Methods for Interpreting and Understanding Deep Neural Networks](https://mlsanity.com/paper/1706.07979/) (2017)
- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [Deep learning to represent sub-grid processes in climate models](https://mlsanity.com/paper/1806.04731/) (2018)
- [Physically Interpretable Neural Networks for the Geosciences: Applications to Earth System Variability](https://mlsanity.com/paper/1912.01752/) (2019)
- [Advancing Parsimonious Deep Learning Weather Prediction using the HEALPix Mesh](https://mlsanity.com/paper/2311.06253/) (2023)
- [Explaining the physics of transfer learning a data-driven subgrid-scale closure to a different turbulent flow](https://mlsanity.com/paper/2206.03198/) (2022)
- [Physical invariance in neural networks for subgrid-scale scalar flux modeling](https://mlsanity.com/paper/2010.04663/) (2020)
- [Learning Closed-form Equations for Subgrid-scale Closures from High-fidelity Data: Promises and Challenges](https://mlsanity.com/paper/2306.05014/) (2023)
- [Machine Learning Global Simulation of Nonlocal Gravity Wave Propagation](https://mlsanity.com/paper/2406.14775/) (2024)

## Abstract (arXiv)

Machine learning (ML) techniques, especially neural networks (NNs), have shown promise in learning subgrid-scale parameterizations for climate models. However, a major problem with data-driven parameterizations, particularly those learned with supervised algorithms, is model instability. Current remedies are often ad-hoc and lack a theoretical foundation. Here, we combine ML theory and climate physics to address a source of instability in NN-based parameterization. We demonstrate the importance of learning spatially textitnon-local dynamics using a 1D model of the quasi-biennial oscillation (QBO) with gravity wave (GW) parameterization as a testbed. While common offline metrics fail to identify shortcomings in learning non-local dynamics, we show that the concept of receptive field (RF) can identify instability a-priori. We find that NN-based parameterizations that seem to accurately predict GW forcings from wind profiles (R2 ≈ 0.99) cause unstable simulations when RF is too small to capture the non-local dynamics, while NNs of the same size but large-enough RF are stable. We examine three broad classes of architectures, namely convolutional NNs, Fourier neural operators, and fully-connected NNs; the latter two have inherently large RFs. We also demonstrate that learning non-local dynamics is crucial for the stability and accuracy of a data-driven spatiotemporal emulator of the zonal wind field. Given the ubiquity of non-local dynamics in the climate system, we expect the use of effective RF, which can be computed for any NN architecture, to be important for many applications. This work highlights the necessity of integrating ML theory with physics to design and analyze data-driven algorithms for weather and climate modeling.