In networked dynamical systems, the parameter of primary mechanistic interest is signed interaction structure.
Recovering this structure from perturbation time-series data is a fundamental identification problem, compounded by three coupled obstacles:
- the combinatorial complexity of interaction architectures,
- ambiguity of causal attribution under limited interventions,
- and state-dependent dynamics that confound structural inference.
Each obstacle is structural in origin and calls for a structural solution.
We address these challenges by adopting a reductionist approach, introducing Fundamental Dynamical Units (FDUs): signed three-node interaction patterns as composable primitives that convert the interaction hypothesis space into a finite, constructive, and tractable representation.
We show that local interaction structure determines the perturbation conditions required to disentangle direct from relayed influence, making intervention design a structural consequence of the FDU representation.
We embed FDU-regularized structural inference within a physics-informed neural ordinary differential equation (ODE) whose governing-equation constraint transforms structural hypotheses into verifiable dynamical predictions, enabling joint recovery of interaction structure and perturbation-resolved trajectories.
Validated on synthetic benchmarks with known ground truth, the framework supports structural commitment, expressed through FDU primitives, motif-prescribed intervention design, and physics-informed learning, as a principled basis for mechanistically interpretable inference in networked dynamical systems.