# Matevž Jug: Learning macroscopic equations of motion from particle-based simulations of a fluid

Equations describing the macroscopic dynamics of complex materials are traditionally derived by a systematic symmetry-based approach. A model derived in this way usually contains a number of unknown parameters that have to be estimated from data; either from experiments or simulations. With a suitable regression method, not only the parameters, but also the dynamic equations themselves can be extracted directly from data, bypassing the need for a traditional derivation. In this talk, I will present such a method, based on the SINDy (Sparse Identification of Nonlinear Dynamics) framework, a weak formulation of the dynamics and a novel model selection measure. Using this method, we were able to extract partial differential equations governing the dynamics of a simple fluid from simulations based on a particle model -- dissipative particle dynamics. These equations were the mass continuity equation and a form of the Navier-Stokes equation, the latter containing the correct pressure equation of state. The talk is based on our recently published article (https://doi.org/10.1016/j.cma.2024.117379).