Mathematical Colloquium

 

Tuesday, Jul 8, 2014, 06:00 pm

Breaking the curse of dimensionality in solving parametric and stochastic PDEs

Prof. Dr. Dr. h.c. Ronald A. DeVore (Texas A&M University)

Abstract:
Approximating functions defined on a space of high dimension is subjected to the so called "curse of dimensionality". This curse says that knowing only that the function is smooth, i.e., highly differentiable, in and of itself will not be enough to guarantee that the function can be accurately approximated with a reasonable number of queries or computations when the domain dimension is large. This has led to new notions such as sparsity, variable reduction, tensor formats, etc., as possible assumptions to make on the function in order to avoid the curse.

We will discuss this problem for the particular case where the function F to be approximated is the solution operator for parametric pdes. This function is not only high dimensional when the number of parameters is large but it is also Banach space valued. Our goal in the talk will be to explain why such notions as reduced modeling and reduced basis are effective for these problems.

Time: 06:00 pm

Location: Hörsaal III, Hauptgebäude, RWTH Aachen, Templergraben 55, 52062 Aachen