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Characterizing information loss in a chaotic double pendulum with the Information Bottleneck
Kieran Murphy · Danielle S Bassett

A hallmark of chaotic dynamics is the loss of information with time. Although information loss is often expressed through a connection to Lyapunov exponents---valid in the limit of high information about the system state---this picture misses the rich spectrum of information decay across different levels of granularity. Here we show how machine learning presents new opportunities for the study of information loss in chaotic dynamics, with a double pendulum serving as a model system. We use the Information Bottleneck as a training objective for a neural network to extract information from the state of the system that is optimally predictive of the future state after a prescribed time horizon. We then decompose the optimally predictive information by distributing a bottleneck to each state variable, recovering the relative importance of the variables in determining future evolution. The framework we develop is broadly applicable to chaotic systems and pragmatic to apply, leveraging data and machine learning to monitor the limits of predictability and map out the loss of information.

Author Information

Kieran Murphy (University of Pennsylvania)
Danielle S Bassett (University of Pennsylvania)

Prof. Bassett is the J. Peter Skirkanich Professor at the University of Pennsylvania, with appointments in the Departments of Bioengineering, Electrical & Systems Engineering, Physics & Astronomy, Neurology, and Psychiatry. Bassett is also an external professor of the Santa Fe Institute. Bassett is most well-known for blending neural and systems engineering to identify fundamental mechanisms of cognition and disease in human brain networks. Bassett is currently writing a book for MIT Press entitled Curious Minds, with co-author Perry Zurn Professor of Philosophy at American University. Bassett received a B.S. in physics from Penn State University and a Ph.D. in physics from the University of Cambridge, UK as a Churchill Scholar, and as an NIH Health Sciences Scholar. Following a postdoctoral position at UC Santa Barbara, Bassett was a Junior Research Fellow at the Sage Center for the Study of the Mind. Bassett has received multiple prestigious awards, including American Psychological Association's ‘Rising Star’ (2012), Alfred P Sloan Research Fellow (2014), MacArthur Fellow Genius Grant (2014), Early Academic Achievement Award from the IEEE Engineering in Medicine and Biology Society (2015), Harvard Higher Education Leader (2015), Office of Naval Research Young Investigator (2015), National Science Foundation CAREER (2016), Popular Science Brilliant 10 (2016), Lagrange Prize in Complex Systems Science (2017), Erdos-Renyi Prize in Network Science (2018), OHBM Young Investigator Award (2020), AIMBE College of Fellows (2020). Bassett is the author of more than 300 peer-reviewed publications, which have garnered over 24,000 citations, as well as numerous book chapters and teaching materials. Bassett is the founding director of the Penn Network Visualization Program, a combined undergraduate art internship and K-12 outreach program bridging network science and the visual arts. Bassett’s work has been supported by the National Science Foundation, the National Institutes of Health, the Army Research Office, the Army Research Laboratory, the Office of Naval Research, the Department of Defense, the Alfred P Sloan Foundation, the John D and Catherine T MacArthur Foundation, the Paul Allen Foundation, the ISI Foundation, and the Center for Curiosity.

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