Deep Learning for Koopman Operator Estimation in Idealized Atmospheric Dynamics
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.
Code (1)
Tasks
Deep LearningWeather ForecastingSimilar Papers 제목 키워드 기반
PyKoopman: A Python Package for Data-Driven Approximation of the Koopman Operator
PyKoopman is a Python package for the data-driven approximation of the Koopman operator associated with a dynamical system. The Koopman operator is a principled linear embedding of nonlinear dynamics and facilitates the …
Koopman Operator in the Weighted Function Spaces and its Learning for the Estimation of Lyapunov and Zubov Functions
The mathematical properties and data-driven learning of the Koopman operator, which represents nonlinear dynamics as a linear mapping on a properly defined functional spaces, have become key problems in nonlinear system …
Ensemble forecasts in reproducing kernel Hilbert space family
A methodological framework for ensemble-based estimation and simulation of high dimensional dynamical systems such as the oceanic or atmospheric flows is proposed. To that end, the dynamical system is embedded in a famil…
Physics-informed Deep Mixture-of-Koopmans Vehicle Dynamics Model with Dual-branch Encoder for Distributed Electric-drive Trucks
Advanced autonomous driving systems require accurate vehicle dynamics modeling. However, identifying a precise dynamics model remains challenging due to strong nonlinearities and the coupled longitudinal and lateral dyna…
Autonomous DrivingKoopman Invariants as Drivers of Emergent Time-Series Clustering in Joint-Embedding Predictive Architectures
Joint-Embedding Predictive Architectures (JEPAs), a powerful class of self-supervised models, exhibit an unexplained ability to cluster time-series data by their underlying dynamical regimes. We propose a novel theoretic…
Self-Supervised Learning