# Fundamental Dynamical Units for Physics-Informed Structural Inference from Perturbation Time-Series in Networked Systems

arXiv: https://arxiv.org/abs/2609.11934 · HTML: https://mlsanity.com/paper/2609.11934/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 49 references that are in the map.
- First posted on arXiv 12 Jun 2026.

## Builds on (most cited first, 13 of 13)

- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Sparse Sequence-to-Sequence Models](https://mlsanity.com/paper/1905.05702/) (2019)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [Learning Continuous System Dynamics from Irregularly-Sampled Partial Observations](https://mlsanity.com/paper/2011.03880/) (2020)
- [Conditional Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/2106.11083/) (2021)
- [Inferring dynamic regulatory interaction graphs from time series data with perturbations](https://mlsanity.com/paper/2306.07803/) (2023)
- [Interpretable Neural ODEs for Gene Regulatory Network Discovery under Perturbations](https://mlsanity.com/paper/2501.02409/) (2025)
- [Inference of dynamical gene regulatory networks from single-cell data with physics informed neural networks](https://mlsanity.com/paper/2401.07379/) (2024)

## Abstract (arXiv)

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.