Department of MathematicsProject leaders: Professor Sayan Mukherjee and Gugan Thoppe
Project manager: Justin Silverman
Team members: Irina Cristali, Matheus Dias, and Peter Hase
Project summary:
We studied stochastic dynamical systems, the models often used to control the movements of robots and drones, understand neural activity in the brain, or even predict the behavior of financial stock markets. Although our models are defined through precise equations, we cannot always predict and understand their overall behavior. For instance, if the system’s parameters are changing over time according to a probability rule, the model might yield erratic outputs. Even if the parameters are fixed, small differences in the initial conditions could also lead to large differences in the outputs. We thus mathematically quantified how complex some frequently-used dynamical systems are, and how this complexity affects our ability to determine the rules governing the systems. We found that our systems met some conditions for high complexity which imply that their rules are hard to learn from observations.