Abstract:
There are many problems in science and engineering where one needs
to estimate the solution of uncertain equations with uncertain or incomplete
data. I will present examples, in particular, the estimation of model parameters
from noisy data (as in the modeling of diffusion), inference
from stochastic differential equations supplemented by a stream of noisy
data (as in economics, robotics, and weather prediction), and
inference from underresolved approximations (as in uncertainty
quantification and model reduction). I will discuss why predictions fail,
the conditions under which such problems can be solved in principle
and in practice, and some open problems. |