Earth System Symmetries - Geometry, Groups, and Limits of Structure in Machine Learning

Explore how geometric and algebraic concepts can enhance machine learning applications for Earth system data in this 25-minute conference talk. Discover why Earth data typically exists in non-Euclidean spaces rather than standard Euclidean frameworks, examining everything from spherical geometry to conservation laws and multi-scale invariance. Learn practical applications of Riemannian geometry for improving training processes, loss functions, and model architecture design when working with data on spheres, Lie groups, positive semidefinite matrices, and discrete topological domains like graphs. Investigate symmetry and invariance through group actions, understanding how these mathematical structures can be leveraged in deep learning models. Examine the limitations of invariant and symmetry-preserving approaches, gaining insights into design principles for determining which mathematical structures to preserve, which to relax, and when symmetry becomes a constraint rather than an advantage in Earth system modeling.