Modern Perspectives in Applied Mathematics: Theory and Numerics of PDEs

Computing with uncertainty

Alexandre Chorin

University of California-Berkeley


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.