Operator-Theoretic Approaches to Feature Extraction and Statistical Modeling of Climate Dynamics

Learn operator-theoretic approaches to feature extraction and statistical modeling of climate dynamics in this 51-minute conference talk from IPAM's Mathematics and Machine Learning for Earth System Simulation Workshop. Explore how operator-theoretic techniques have revolutionized analysis and data-driven modeling of dynamical systems over the past three decades by leveraging the linearity of nonlinear dynamics on spaces of observables or probability distributions through Koopman or transfer operators. Discover the mathematical formulation of data-driven dynamical operator methods and their applications to climate dynamics spanning daily to interannual timescales. Examine kernel methods for consistent operator approximation in both supervised and unsupervised learning problems, with practical demonstrations including extraction and prediction of the El Niño Southern Oscillation and dynamical closure in cloud-resolving atmospheric models. Gain insights into spectral decomposition, forecasting, and uncertainty quantification techniques for complex climate systems through this comprehensive survey of cutting-edge mathematical approaches to Earth system modeling.