## Research Abstracts Online

January 2010 - March 2011

Main TOC ...... Next Abstract

### University of Minnesota Twin Cities

College of Biological Sciences

Department of Ecology, Evolution, and Behavior

# PI: Clarence L. Lehman

### Numerical Modeling With and Without Governing Equations

Given computers of sufficient capacity, dynamical systems can be analyzed and simulated by directly modeling their myriad individual parts, rather than first abstracting to a mathematical form and then analyzing the mathematics. This can reduce intellectual complexity and thereby increase the range of problems that can be understood with the aid of computation. These researchers are developing new methods of modeling using real-world, large-scale problems in ecology, epidemiology, and economics. The methods involve: substituting inverse cumulative probability distributions for probability density functions to cast certain events into the simulated future and thereby avoid unnecessary computer cycles during each incremental time step; allowing other events to drift into the simulated past, to be examined only at a future time if and when they are needed; and integrating with standard mathematical-numerical methods where those methods are best. The researchersâ€™ prototype systems run many orders of magnitude faster than classical approaches. Access to large-scale computers is necessary at this stage to extend the scope of their epidemiological models to entire nations, where tens or hundreds of millions of individuals must be separately tracked.

### Group Member

Adrienne Keen, Graduate Student