Visualization & Optimization Techniques For Analysis and Design of Complex Systems

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

This project concerns several interrelated approaches to managing complexity in large interconnected systems. Specific application areas addressed in the proposal include phase transitions in molecular models, and resource allocation in large network models. Ideally, we wish to build a collection of 'microscopes' that allow us to view these systems on various scales, and filter away irrelevant information. The PI has recently developed methods that are intended to perform exactly this task. Over the proposed funding period he will develop these and new approaches for addressing visualization and optimization problems in complex systems. Specific analytical approaches to be developed include, (i) Relaxation techniques based upon separation of fast and slow time-scales. This involves 'workload-relaxations' in the network domain, and recent approaches to spectral theory for diffusion models. (ii) General theory of Markov processes and diffusion models, especially recent results concerning large deviations theory and entropy. (iii) Methods for including prior knowledge to speed simulation and on-line learning for complex stochastic models, and for predicting and simulating rare events. (iv) Extend fluid model techniques for addressing control and sensitivity in network optimization in realistic settings. The PI will collaborate with graduate students at Illinois, researchers in applied mathematics at Brown University, and others in computer science and physics at research institutes in Germany. The expected impact of this research is far-reaching, and it is likely that cross-fertilization between all of these mathematical and application areas will be significant. In networks applications, these results will provide new methods for providing intuition about the behavior of large networks, new approaches to design, and efficient approaches to simulation and on-line tuning of policies. If successful, the research on spectral theory and diffusions will provide alternative-modeling techniques for molecular systems that capture essential dynamics and can be easily simulated.