  Many complex systems are composed of interacting parts, and the underlying
laws are usually simple and universal. While graph neural networks provide a
useful relational inductive bias for modeling such systems, generalization to
new system instances of the same type is less studied. In this work we trained
graph neural networks to fit time series from an example nonlinear dynamical
system, the belief propagation algorithm. We found simple interpretations of
the learned representation and model components, and they are consistent with
core properties of the probabilistic inference algorithm. We successfully
identified a 'graph translator' between the statistical interactions in belief
propagation and parameters of the corresponding trained network, and showed
that it enables two types of novel generalization: to recover the underlying
structure of a new system instance based solely on time series observations, or
to construct a new network from this structure directly. Our results
demonstrated a path towards understanding both dynamics and structure of a
complex system and how such understanding can be used for generalization.
