MeGA-MP: Metric Graph Advection Message Passing -- A Physics-Informed Message Passing Operator for Advection-Dominated Metric Graphs

arXiv:2607.05167v1 Announce Type: new Abstract: Many real-world systems are organized as networks where spatio-temporal dynamics unfold along connections and not discretely between nodes. Examples include utility networks such as water distribution systems or gas networks, electrical grids, and traffic flow networks. Such systems are naturally modeled as metric graphs, where edges correspond to one-dimensional Euclidean subspaces connected at vertices. Metric graphs are independent of an underlying global Euclidean space, limiting direct application of typical PINNs and operator-learning metho