### Jorge Cortés

#### Professor

Dynamics of data-driven ambiguity sets for hyperbolic conservation laws with uncertain inputs

F. Boso, D. Boskos, J. Cortés, S. Martínez, D. M. Tartakovsky

SIAM Journal on Scientific Computing, submitted

### Abstract

Ambiguity sets of probability distributions are used to
hedge against uncertainty about the true probabilities
of random quantities of interest (QoIs). When available,
these ambiguity sets are constructed from both data
(collected at the initial time and along the boundaries
of the physical domain) and concentration-of-measure
results on the Wasserstein metric. To propagate the
ambiguity sets into the future, we use a
physics-dependent equation governing the evolution of
cumulative distribution functions (CDF) obtained through
the method of distributions. This study focuses on the
latter step by investigating the spatio-temporal
evolution of data-driven ambiguity sets and their
associated guarantees when the random QoIs they describe
obey hyperbolic partial-differential equations with
random inputs. For general nonlinear hyperbolic
equations with smooth solutions, the CDF equation is
used to propagate the upper and lower envelopes of
pointwise ambiguity bands. For linear dynamics, the CDF
equation allows us to construct an evolution equation
for tighter ambiguity balls. We demonstrate that, in
both cases, the ambiguity sets are guaranteed to contain
the true (unknown) distributions within a prescribed
confidence.

pdf

Mechanical and Aerospace Engineering,
University of California, San Diego

9500 Gilman Dr,
La Jolla, California, 92093-0411

Ph: 1-858-822-7930

Fax: 1-858-822-3107

cortes at ucsd.edu

Skype id:
jorgilliyo