Differential Analysis for Networks Obeying Conservation Laws

by   Anirudh Rayas, et al.

Networked systems that occur in various domains, such as the power grid, the brain, and opinion networks, are known to obey conservation laws. For instance, electric networks obey Kirchoff's laws, and social networks display opinion consensus. Such conservation laws are often modeled as balance equations that relate appropriate injected flows and potentials at the nodes of the networks. A recent line of work considers the problem of estimating the unknown structure of such networked systems from observations of node potentials (and only the knowledge of the statistics of injected flows). Given the dynamic nature of the systems under consideration, an equally important task is estimating the change in the structure of the network from data – the so called differential network analysis problem. That is, given two sets of node potential observations, the goal is to estimate the structural differences between the underlying networks. We formulate this novel differential network analysis problem for systems obeying conservation laws and devise a convex estimator to learn the edge changes directly from node potentials. We derive conditions under which the estimate is unique in the high-dimensional regime and devise an efficient ADMM-based approach to perform the estimation. Finally, we demonstrate the performance of our approach on synthetic and benchmark power network data.


page 1

page 2

page 3

page 4


Learning the Structure of Large Networked Systems Obeying Conservation Laws

Many networked systems such as electric networks, the brain, and social ...

A new technique for preserving conservation laws

In this paper we introduce a new symbolic-numeric strategy to obtain sem...

Invariant finite-difference schemes with conservation laws preservation for one-dimensional MHD equations

Invariant finite-difference schemes are considered for one-dimensional m...

Exact conservation laws for neural network integrators of dynamical systems

The solution of time dependent differential equations with neural networ...

AI Poincaré 2.0: Machine Learning Conservation Laws from Differential Equations

We present a machine learning algorithm that discovers conservation laws...

Tractable learning in under-excited power grids

Estimating the structure of physical flow networks such as power grids i...

Gradient-based Monte Carlo methods for relaxation approximations of hyperbolic conservation laws

Particle methods based on evolving the spatial derivatives of the soluti...

Please sign up or login with your details

Forgot password? Click here to reset