A demonstration and methodological adaptation showing that the Weak-form Sparse Identification of Nonlinear Dynamics (WSINDy) algorithm can discover interpretable, symbolic partial differential equations governing atmospheric and geophysical phenomena from noisy data. Rather than fitting opaque neural networks, WSINDy convolves a library of candidate terms against compactly-supported test functions (a weak formulation that damps noise) and uses sparse regression to select a parsimonious governing equation. The contribution adapts standard WSINDy to high-dimensional fluid data of arbitrary spatial dimension and validates it on three simulated geophysical datasets and on global-scale ECMWF assimilated reanalysis data, recovering physically interpretable atmospheric models.
Data-driven weather modeling has surged, but most approaches use highly parameterized neural networks that are uninterpretable and yield limited scientific understanding. This paper addresses interpr…