We introduce a principled approach for jointly recovering the underlying networkstructure and dynamic response of a physical system. We show that our simulation-free method,NGM-SF2M, not only exhibits improved scaling relative to NGM on progressively larger linearsystems, but also consistently retrieves a competitive recovery of the underlying network structure.Moreover, we show that incorporating interventional data yields improved performance for inferringnetwork interactions. Our results indicate that while RF recovers marginally more accurate networkstructure, NGM-SF2M yields improved performance on the joint task – dynamical inference andstructure learning. In future work, we aim to extend our framework to higher-dimensional systems,real-world settings, and integrate multi-modal data such as chromatin accessibility.