MULTISCALE DYNAMICS AND EXTREME EVENTS IN COMPLEX SYSTEMS AND NETWORKS CONTAINING MANY INTERACTING HETEROGENEOUS COMPONENTS
Abstract
This project addresses the urgent need that exists for a mathematical theory of the complex, multiscale dynamics, including extreme and rare events, that arise in systems and networks comprising a time-dependent number of interacting, heterogeneous, and possibly adaptive components. These components may include machines, sensors, algorithms, humans and ultimately an Internet-of-Things, with anywhere from tens to many millions of components acting at any one time. Such systems are of interest to DoD, to broader society, and may already be being weaponized by U.S. adversaries. Such unexpected extreme behaviors (e.g. rare events) can generate unmitigated risks to mission-critical systems in terms of safety, performance and security. The project approaches this urgent challenge in a way that complements and extends existing computational mathematics research, by profiting from tools from many-body physics, including the key concepts of renormalization, scaling and self-organized criticality, to include variable numbers (from tens to millions) of interacting objects and to account for their intrinsic heterogeneity. The project sacrifices a detailed description of the individual objects or their specific number, for a broader, system-level description of the out-of-equilibrium dynamics including the sudden emergence of extremes beyond mean-field. It goes beyond descriptions of a system s typical, or steady-state, or equilibrium behavior which can be treated using mean-field theories that average over populations or over time. It treats explicitly how the interacting clusters of heterogeneous pieces from one scale emerge in time and can then be embodied into a single ‘composite agent’ at the next scale. Appropriate approximations are then introduced in order to re-package this composite agent’s new internal degrees of freedom and new interactions
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2021
- Source ID
- FA95502010383
Entities
People
- Neil F. Johnson
Organizations
- Air Force Office of Scientific Research
- George Washington University
- United States Air Force