Scalable Discovery of Fundamental Physical Laws: Learning Magnetohydrodynamics from 3D Turbulence Data

Abstract: The discovery of dynamical models from data represents a crucial step in advancing our understanding of physical systems. Library-based sparse regression has emerged as a powerful method for inferring governing equations directly from spatiotemporal data, but current model-agnostic implementations remain computationally expensive, limiting their applicability to data that lack substantial complexity. To overcome these challenges, we introduce a scalable framework that enables efficient discovery of complex dynamical models across a wide range of applications. We demonstrate the capabilities of our approach, by ``discovering'' the equations of magnetohydrodynamics (MHD) from synthetic data generated by high-resolution simulations of turbulent MHD flows with viscous and Ohmic dissipation. Using a library of candidate terms that is $\gtrsim 10$ times larger than those in previous studies, we accurately recover the full set of MHD equations, including the subtle dissipative terms that are critical to the dynamics of the system. Our results establish sparse regression as a practical tool for uncovering fundamental physical laws from complex, high-dimensional data without assumptions on the underlying symmetry or the form of any governing equation.