Data-Driven Discovery of Fluid Dynamics Equations from Spatial-Temporal Data

Abstract: Extracting fundamental physical laws from complex spatio-temporal data is a critical challenge in scientific discovery. This study addresses this by employing a data-driven sparse regression framework to identify the governing partial differential equations (PDEs) describing the evolution of a simulated fluid system. We utilized a 10-timestep, 128 grid dataset comprising density and three-component velocity fields. Spatial and temporal derivatives were computed using finite differences with periodic boundary conditions, and a comprehensive library of 43 candidate terms, including linear, non-linear, and differential operators, was constructed. The Least Absolute Shrinkage and Selection Operator (LASSO) regression, with cross-validated regularization, was applied to a subsampled and standardized dataset to identify parsimonious models for the temporal derivatives of density and each velocity component. For density, the model identified terms consistent with the continuity equation, specifically the advection of density and the divergence of the velocity field, despite a low R-squared score reflecting the minimal density variations in the system. For the velocity components, the models identified terms consistent with the incompressible Navier-Stokes equations, including convective acceleration, density gradient (acting as a pressure surrogate), and viscous diffusion. These models achieved R-squared scores ranging from 0.58 to 0.73 on unseen test data, indicating robust generalization. Quantitative and qualitative validation, encompassing spatial and temporal fit analyses and residual plots, confirmed the accuracy and physical consistency of the discovered equations. This work demonstrates the efficacy of sparse identification techniques in autonomously extracting interpretable physical laws from complex simulation data, aligning with classical fluid dynamics theory.

Subjects:	physics.flu-dyn; physics.comp-ph; physics.data-an; cs.LG
Cite as:	PX:2604.00036