Deep Learning for Koopman Operator Estimation in Idealized Atmospheric Dynamics

2024/09/10 by David E. Millard, Millard, David, Arielle Carr +3
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Atmospheric and Oceanic Physics (physics.ao-ph) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Machine Learning (cs.LG) #Meteorological Phenomena and Simulations #Model Reduction and Neural Networks

paper · pdf · doi:10.48550/arxiv.2409.06522

openalex publication_date 2024/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictors
• Koopman Invertible Autoencoder: Leveraging Forward and Backward Dynamics for Temporal Modeling
• Temporally Consistent Koopman Autoencoders for Forecasting Dynamical Systems
• Leveraging Neural Koopman Operators to Learn Continuous Representations of Dynamical Systems from Scarce Data
• Analyzing Koopman approaches to physics-informed machine learning for long-term sea-surface temperature forecasting