### Joint-sparse recovery for high-dimensional parametric PDEs

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, March 5, 2018 - 13:55 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Nick Dexter – University of Tennessee – ndexter@utk.edu

We present and analyze a novel sparse polynomial approximation method
for the solution of PDEs with stochastic and parametric inputs. Our
approach treats the parameterized problem as a problem of joint-sparse
signal reconstruction, i.e.,
the simultaneous reconstruction of a set of signals sharing a common
sparsity pattern from a countable, possibly infinite, set of
measurements. Combined with the standard measurement scheme developed
for compressed sensing-based polynomial approximation, this
approach allows for global approximations of the solution over both
physical and parametric domains. In addition, we are able to show that,
with minimal sample complexity, error estimates comparable to the best
s-term approximation, in energy norms, are achievable,
while requiring only a priori bounds on polynomial truncation error. We
perform extensive numerical experiments on several high-dimensional
parameterized elliptic PDE models to demonstrate the superior recovery
properties of the proposed approach.