# Physics Informed Topology Learning in Networks of Linear Dynamical Systems

arXiv: https://arxiv.org/abs/1809.10535 · HTML: https://mlsanity.com/paper/1809.10535/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Sep 2018.

## Built on by (most cited first, 7 of 7)

- [Efficient and passive learning of networked dynamical systems driven by non-white exogenous inputs](https://mlsanity.com/paper/2110.00852/) (2021)
- [Learning Distribution Grid Topologies: A Tutorial](https://mlsanity.com/paper/2206.10837/) (2022)
- [Information Theoretically Optimal Sample Complexity of Learning Dynamical Directed Acyclic Graphs](https://mlsanity.com/paper/2308.16859/) (2023)
- [Network Topology Inference from Smooth Signals Under Partial Observability](https://mlsanity.com/paper/2410.05707/) (2024)
- [Learning the Structure of Large Networked Systems Obeying Conservation Laws](https://mlsanity.com/paper/2206.07083/) (2022)
- [Causal Structure Recovery of Linear Dynamical Systems: An FFT based Approach](https://mlsanity.com/paper/2309.02571/) (2023)
- [Multi-Agent System Identification with Nonlinear Sheaf Diffusion](https://mlsanity.com/paper/2605.11204/) (2026)

## Abstract (arXiv)

Learning influence pathways of a network of dynamically related processes from observations is of considerable importance in many disciplines. In this article, influence networks of agents which interact dynamically via linear dependencies are considered. An algorithm for the reconstruction of the topology of interaction based on multivariate Wiener filtering is analyzed. It is shown that for a vast and important class of interactions, that respect flow conservation, the topology of the interactions can be exactly recovered. The class of problems where reconstruction is guaranteed to be exact includes power distribution networks, dynamic thermal networks and consensus networks. The efficacy of the approach is illustrated through simulation and experiments on consensus networks, IEEE power distribution networks and thermal dynamics of buildings.