[Submitted on 12 Jun 2026]
Title:Fundamental Dynamical Units for Physics-Informed Structural Inference from Perturbation Time-Series in Networked Systems
View a PDF of the paper titled Fundamental Dynamical Units for Physics-Informed Structural Inference from Perturbation Time-Series in Networked Systems, by Nima Nouri
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Abstract: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.
Subjects:
Machine Learning (cs.LG); Computational Physics (physics.comp-ph)
Cite as: arXiv:2609.11934 [cs.LG]
(or arXiv:2609.11934v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.11934
arXiv-issued DOI via DataCite
Submission history
From: Nima Nouri [view email] [v1] Fri, 12 Jun 2026 11:58:37 UTC (6,424 KB)
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