Applied Mathematics Colloquium

Due to lack of scientific understanding, some mechanisms are not always well- represented in mathematical models for complex systems. The impact of these uncertain mechanisms on the overall system evolution may be delicate or even profound. These uncertain mechanisms are sometimes microscopic, and it is desirable to examine how they affect the system at the macroscopic level since we are often mainly interested in macroscopic dynamics.

The speaker presents an overview of several available analytical and computational techniques for extracting macroscopic dynamics, while taking uncertain microscopic mechanisms into account. The issues include quantifying uncertain mechanisms via probability distributions, dynamical averaging of random slow-fast microscopic mechanisms, ensemble averaging of fluctuating driving forces, and especially, data-driven quantification of uncertain mechanisms in water vapor dynamics.