# Deep Learning for Koopman Operator Estimation in Idealized Atmospheric Dynamics

arXiv: https://arxiv.org/abs/2409.06522 · HTML: https://mlsanity.com/paper/2409.06522/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 20 references that are in the map.
- First posted on arXiv 10 Sep 2024.

## Builds on (most cited first, 7 of 7)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [Pangu-Weather: A 3D High-Resolution Model for Fast and Accurate Global Weather Forecast](https://mlsanity.com/paper/2211.02556/) (2022)
- [CKNet: A Convolutional Neural Network Based on Koopman Operator for Modeling Latent Dynamics from Pixels](https://mlsanity.com/paper/2102.10205/) (2021)

## Built on by (most cited first, 2 of 2)

- [PEARL: Preconditioner Enhancement through Actor-critic Reinforcement Learning](https://mlsanity.com/paper/2501.10750/) (2025)
- [A Dynamic Weighting Strategy to Mitigate Worker Node Failure in Distributed Deep Learning](https://mlsanity.com/paper/2409.09242/) (2024)

## Abstract (arXiv)

Deep learning is revolutionizing weather forecasting, with new data-driven models achieving accuracy on par with operational physical models for medium-term predictions. However, these models often lack interpretability, making their underlying dynamics difficult to understand and explain. This paper proposes methodologies to estimate the Koopman operator, providing a linear representation of complex nonlinear dynamics to enhance the transparency of data-driven models. Despite its potential, applying the Koopman operator to large-scale problems, such as atmospheric modeling, remains challenging. This study aims to identify the limitations of existing methods, refine these models to overcome various bottlenecks, and introduce novel convolutional neural network architectures that capture simplified dynamics.