## Structure Learning in Critical Infrastructure Networks

This is the public website for the graduate summer course on ‘Structure Learning in Critical Infrastructure Networks.’ This course is part of the Graduate School in Systems, Optimization, Control and Networks (SOCN).

## Lecturer

Rajasekhar Anguluri

Assistant Professor

University of Maryland, Baltimore County

Email: rajangul(at)umb(dot)edu

## Course description

Critical infrastructure networks are important assets in our society. Examples include power, water, transportation, and communication systems. The knowledge of structure (connectivity of nodes in the network) is crucial for implementing real-time decision-making algorithms. However, due to practical limitations, such knowledge is either partially or fully unavailable. Lately, many structure learning methods have been proposed to overcome this limitation. This workshop aims to provide some of the important methodological ideas in an introductory manner. A Detailed list of topics is on the second page.

## Key learning outcomes

Basics of modelling infrastructure networks using equilibrium equations.

Basic understating of estimating linear and covariance models with sparsity constraints, and their relevance to infrastructure networks.

Algorithmic techniques such as alternating direction method of multipliers (ADMM) for structure learning problems.

## Prerequisites

Basic concepts in Linear Algebra, optimization, and probability.

## About the instructor

Rajasekhar Anguluri is an assistant professor in the Department of Computer Science and Electrical Engineering at the University of Maryland, Baltimore County, USA. He holds the Ph.D. degree in Mechanical Engineering, and the master’s degree in Statistics from the University of California, Riverside, USA. He was a 2022-2023 Mistletoe Research fellow. He enjoys taking weird selfies (as shown on the side).

His research centers on systems theory and statistical signal/data processing. He develops interpretable solutions for inference problems (e.g. estimation and security) in cyber-physical networks by making non-interpretable assumptions.

## Schedule

The tentative schedule is as follows.

Learning problem in Infrastructure networks (July 3, 9:30-11:00 AM)

Introduction to Graphs and Kirchhoff’s conservation laws

Explicit modeling examples from power and water network systems

Measurementmodelsandpartialobservability

Structure learning framework: linear and covariance models

Sparse estimation: some theory and algorithms (July 4, 9:30-11:30 AM)

Sparse linear regression problem

Sparse inverse covariance estimation problem

ADMM algorithm to solve both estimation problems

Python or MATLAB demonstration/tutorial

Learning structure in sparse infrastructure networks (July 5, 9:30-11:00 AM)

Identifiability conditions including latent variables

Indirect (two-stage) learning method via ADMM

DirectlearningmethodviaADMM

Extensions: differential analysis, stationary time series data.

I will mention a few open problems during the course and provide a lecture- notes before the workshop. These notes contain interesting exercise problems for participants. Senior undergraduate and graduate students with interest in mathematical engineering (e.g., controls, statistical signal processing, network theory, data sciences, and optimization) will benefit from this course.

## Resources

Password: SOCN_anguluri

## Practical information

Duration: 3 lectures of approximately 2 hours each

When: July 3, 4, 5, 2024 from 9:30 am to 11:30 am

Where: UCLouvain - Euler building (room A.002) Avenue Georges Lemaître, 4 - 1348 Louvain la Neuve

Travel instructions are available here

## Course registration

For organizational reasons, registration is mandatory for all attendees.

There is no registration fee for participants from SOCN partners institutions (UAntwerpen, VUB, ULB, UGent, KU Leuven, ULiège, UCLouvain, UMONS, UNamur).

For additional details, please visit this page

Please register here

## Organizers

**Gianluca Bianchin**

Assistant professor

UC Louvain

**Rajasekhar Anguluri**

Assistant professor

University of Maryland