Fundamental Dynamical Units for Physics-Informed Structural Inference from Perturbation Time-Series in Networked Systems
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.
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BibTeX
@misc{nouri2026fundamental,
title = {{Fundamental Dynamical Units for Physics-Informed Structural Inference from Perturbation Time-Series in Networked Systems}},
author = {Nima Nouri},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11934},
eprint = {2609.11934},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11934},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fundamental Dynamical Units for Physics-Informed Structural Inference from Perturbation Time-Series in Networked Systems
AU - Nima Nouri
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.11934
UR - https://arxiv.org/abs/2609.11934
AB - 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.
ER -