  We present a comprehensive examination of learning methodologies employed for
the structural identification of dynamical systems. These techniques are
designed to elucidate emergent phenomena within intricate systems of
interacting agents. Our approach not only ensures theoretical convergence
guarantees but also exhibits computational efficiency when handling
high-dimensional observational data. The methods adeptly reconstruct both
first- and second-order dynamical systems, accommodating observation and
stochastic noise, intricate interaction rules, absent interaction features, and
real-world observations in agent systems. The foundational aspect of our
learning methodologies resides in the formulation of tailored loss functions
using the variational inverse problem approach, inherently equipping our
methods with dimension reduction capabilities.
