Data-Driven Identification of Region-Dependent Pressure Tensor Closures in Turbulent Space Plasmas

Understanding and modelling turbulence in space plasmas requires capturing kinetic effects that go beyond standard fluid closures. In the present work, we present a data-driven framework that combines unsupervised clustering and sparse equation discovery to identify effective closures in turbulent plasmas. Our primary focus is on solar-wind observations, but with possible applications to magnetospheric environments.

We use unsupervised clustering methods, more specifically k-means, to identify dynamically similar regions in both in situ spacecraft data and numerical simulations. The first part of the project is focused on numerical simulations. Clustering is performed on multidimensional feature spaces constructed from plasma moments, fields, and other pressure-tensor-related quantities, applied to either 3D or 2D simulations. The resulting clusters define coherent regions characterized by comparable kinetic activity, anisotropy, and turbulence properties.

These clustered regions serve as domains for sparse identification of nonlinear dynamics (SINDy). Particular emphasis is placed on exploring data-driven closures involving the pressure tensor, including anisotropic and nongyrotropic contributions, and understanding their role in momentum and other dynamical equations.

The framework is designed to function consistently across both in situ measurements, such as Magnetospheric Multiscale (MMS) observations, and PIC simulations, enabling direct validation and comparison. This combined approach provides a structured method for discovering interpretable, region-specific closures in turbulent space plasmas and supports the development of reduced models directly informed by observations.