Inferring Mean-field Models from Microscale Observations - Strengths of a Weak Form

Explore a cutting-edge approach to inferring governing equations from experimental data across multiple scales in this 54-minute conference talk. Discover how weak formulations of differential equations can reveal effective macroscale descriptions from microscale observations, addressing a fundamental challenge in scientific research. Learn about the WSINDy algorithm (Weak-form Sparse Identification of Nonlinear Dynamics) and its ability to handle non-smooth dynamics and noisy data through test function methodologies. Examine how these weak-form inference methods can uncover mean-field and coarse-grained models, and identify microscale rules through their embedding in macroscale equations. Delve into recent applications including inferring interaction rules for migrating cell populations and finding moment closure models and homogenized equations from particle simulations at the boundary between kinetic and hydrodynamic phenomena. Understand how complex macroscale behavior, from cell migration to turbulence, can be reduced to sparse systems of equations describing underlying microscale processes, and explore the reverse engineering approach to derive effective macroscale descriptions from microscale observations.