Physics informed topology learning in networks of linear dynamical systems

Saurav Talukdar, Deepjyoti Deka, Harish Doddi, Donatello Materassi, Michael Chertkov, Murti V. Salapaka

Research output: Contribution to journalArticlepeer-review

Abstract

Learning influence pathways in 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 includes physical systems with flow conservation, the topology of the interactions can be exactly recovered, even for colored exogenous inputs. The efficacy of the approach is illustrated through simulation and experiments on multiple important networks, including consensus networks, IEEE power networks and EnergyPlus based simulation of thermal dynamics of buildings.

Original languageEnglish (US)
Article number108705
JournalAutomatica
Volume112
DOIs
StatePublished - Feb 2020

Bibliographical note

Funding Information:
The authors S. Talukdar, H. Doddi, D. Materassi and M.V. Salapaka acknowledge the support of ARPA-E for supporting this research through the project titled ?A Robust Distributed Framework for Flexible Power Grids? via Grant No. DEAR000071. Authors D. Deka and M. Chertkov acknowledge the support from the Department of Energy through the Grid Modernization Lab Consortium, and the Center for Non Linear Studies (CNLS) at Los Alamos National Laboratory. The material in this paper was presented at the Eighth ACM International Conference on Future Energy Systems, May 16?19, 2017, Shatin, Hong Kong, China; the 56th IEEE Conference on Decision and Control, December 12?15, 2017, Melbourne, Australia; the 57th IEEE Conference on Decision and Control, December 17?19, 2018, Miami Beach, Florida, USA. This paper was recommended for publication in revised form by Associate Editor Julien M. Hendrickx under the direction of Editor Christos G. Cassandras

Funding Information:
Pereira et al., 2010 ) (A.1) { R j i , γ } = arg inf { R j i } i = 1 , … , m , i ≠ j E [ x j ( k ) − ∑ i = 1 , i ≠ j n R j i x i ( k − 1 ) ] 2 + γ ∑ i = 1 , i ≠ j n | R j i | , ≈ arg inf { R j i } i = 1 , … , n , i ≠ j 1 N ∑ k = 0 N ( x j ( k ) − ∑ i = 1 , i ≠ j m R j i x i ( k − 1 ) ) 2 + γ ∑ i = 1 , i ≠ j n | R j i | . Here γ ≥ 0 is the regularization parameter. Saurav Talukdar is a Control Systems and Machine Learning Engineer at Google and focuses on energy optimization for Google Data Center. Prior to joining Google in 2019, he was a Battery Algorithm Engineer at Apple working on system identification and thermal management of Lithium ion batteries in iPhones. He received the B.Tech and M.Tech degrees in Mechanical Engineering from Indian Institute of Technology, Bombay, India in 2013 and Ph.D. degree in Mechanical Engineering from the University of Minnesota, Minneapolis, USA in 2018. Deepjyoti Deka is a staff scientist in the Applied Mathematics and Plasma Physics group of the Theoretical Division at Los Alamos National Laboratory (LANL), where he was previously a postdoctoral research associate at the Center for Nonlinear Studies. His research interests include data-analysis of power grid structure, operations and security, and optimization in social and physical networks. Before joining the laboratory he received the M.S. and Ph.D. degrees in electrical engineering from the University of Texas, Austin, TX, USA, in 2011 and 2015, respectively and his B.Tech degree in Electrical Engineering from IIT Guwahati, India in 2009. Harish Doddi is a Ph.D. candidate in the Mechanical Engineering Department at the University of Minnesota, Minneapolis since 2016. He obtained his B.Tech degree from Indian Institute of Technology Madras, Chennai in 2014 and worked on Thermal Analysis of Commercial Buildings at the TCS Innovation Lab, Chennai, India till 2016. His research includes Information Thermodynamics, Energy limits in Computing and Structure learning of Graphical models. Donatello Materassi holds a Laurea in “In- gegneria Informatica” and a “Dottorato di Ricerca” in Electrical Engineering/Nonlinear Dynamics and Complex Systems from Università degli Studi di Firenze, Italy. He has been a research associate at University of Minnesota (Twin Cities) from 2008 till 2011. He has been concurrently both a post-doctoral researcher at Laboratory for Information and Decision Systems (LIDS) at Massachusetts Institute of Technology and a lecturer at Harvard University FROM 2012–2014. Since 2019, he is an assistant professor at University of Minnesota in Minneapolis. Prior to that, he was an assistant professor at the University of Tennessee, Knoxville. He received the NSF CAREER award in 2015. His research interests include nonlinear dynamics, system identification and classical control theory with applications to atomic force microscopy, single molecule force spectroscopy, biophysics, statistical mechanics and quantitative finance. Michael Chertkov ’s area of focus is mathematics, including statistics and data science, applied to physical, engineered and other systems. Dr. Chertkov received his Ph.D. in physics from the Weizmann Institute of Science in 1996, and his M.Sc. in physics from Novosibirsk State University in 1990. After his Ph.D., Dr. Chertkov spent three years at Princeton University as a R.H. Dicke Fellow in the Department of Physics. He joined Los Alamos National Lab in 1999, initially as a J.R. Oppenheimer Fellow in the Theoretical Division, and continued as a Technical Staff Member. In 2019, Dr. Chertkov joined the University of Arizona as a Professor of Mathematics and leads the Interdisciplinary Graduate Program in Applied Mathematics. He is a fellow of the American Physical Society (APS) and a senior member of IEEE. Murti V. Salapaka received the B.Tech. degree in Mechanical Engineering from the Indian Institute of Technology, Madras, in 1991 and the M.S. and Ph.D. degrees in Mechanical Engineering from the University of California at Santa Barbara, in 1993 and 1997, respectively. He was a faculty member in the Electrical and Computer Engineering Department, Iowa State University, Ames, from 1997 to 2007. Currently, he is the Director of Graduate Studies and the Vincentine Hermes Luh Chair Professor in the Electrical and Computer Engineering Department, University of Minnesota, Minneapolis. His research interests include control and network science, nanoscience and single molecule physics. Dr. Salapaka received the 1997 National Science Foundation CAREER Award and is an IEEE fellow.

Publisher Copyright:
© 2019

Keywords

  • Graphical models
  • Networks
  • Structure learning of time series
  • Topology learning

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