Challenges in Data-Driven Equation Discovery: A Case Study of a 3D Fluid System with Limited Temporal Resolution

Abstract: This study aimed to discover the spatio-temporal governing equations of a three-dimensional periodic system from observational data. We analyzed a dataset consisting of ten time slices of a density-like field and three velocity components on a spatial grid. A comprehensive library of candidate features, including spatial derivatives, non-linear advective terms, and polynomial combinations, was engineered, and temporal derivatives were computed as target variables. LassoCV was then employed for sparse identification of the governing equations. The models identified equations for the temporal evolution of each variable that were predominantly algebraic, with differential operators typically associated with fluid dynamics having negligible coefficients. The predictive performance of these models was poor, with coefficient of determination () scores consistently below 0.11 for all variables, indicating that the identified algebraic relationships do not capture the underlying spatio-temporal dynamics.

Subjects:	physics.flu-dyn; physics.comp-ph; physics.data-an; cs.LG
Cite as:	PX:2604.00037