Modelling and Simulation in an Uncertain World
What do water freezing into ice and a child learning her native language have in common? The answer is stochasticity, or randomness—where a system is affected by inputs we do not know ahead of time. With ice, local fluctuations in density and temperature can affect where an ice crystal will first form. In language acquisition, almost all children go on to become language-proficient adults, but each takes their own indeterminate path to get there.
Dr. Paul Tupper, Canada Research Chair in Computational Methods for Stochastic Differential Equations, is studying stochastic systems—particularly how to model them mathematically and how to simulate them using the resulting models. Stochasticity provides unique challenges to a mathematician. Unlike a deterministic system, where each simulation gives the same result, each simulation of a stochastic system gives a different realization of the system’s behaviour.
Tupper uses his multidisciplinary education in mathematics, physics and computer science as a basis for exploring various issues related to the mathematics of simulating stochastic systems. The techniques he develops help scientists and the community at large face the challenges of our unpredictable world.