Algebraic network reconstruction of discrete dynamical systems

TL;DR

This paper introduces an algebraic method using monomial ideals to accurately reconstruct the network structure of discrete dynamical systems from data, even with noise, under monotonicity assumptions.

Contribution

It provides a novel algebraic approach for reverse engineering network structures of discrete dynamical systems from data, with theoretical guarantees.

Findings

Method accurately reconstructs network diagrams with sufficient data.

Approach is robust to small noise in data.

Theoretical proof of uniqueness of reconstruction.

Abstract

We present a computational algebra solution to reverse engineering the network structure of discrete dynamical systems from data. We use monomial ideals to determine dependencies between variables that encode constraints on the possible wiring diagrams underlying the process generating the discrete-time, continuous-space data. Our work assumes that each variable is either monotone increasing or decreasing. We prove that with enough data, even in the presence of small noise, our method can reconstruct the correct unique wiring diagram.