Department of Computer Science, University of Colorado Boulder
Title
Tools and techniques for subspace-based parameter reduction in computational science models
Abstract
Scientists and engineers use computer simulations to study relationships between a physical model's input
parameters and its output predictions. However, thorough parameter studies - e.g., constructing response surfaces,
optimizing, or averaging - are challenging, if not impossible, when the simulation is expensive and the model has several
inputs. To enable parameter studies in these instances, the engineer may attempt to reduce the dimension
of the model's input parameter space using techniques such as sensitivity analysis or variable screening to
identify unimportant variables that can be fixed for model analysis. Generalizing classical coordinate-based reduction,
there are several emerging subspace-based parameter reduction tools, such as active subspace and sufficient dimension
reduction, that identify important directions in the input parameter space with respect to a particular model
output. I will motivate and provide an overview of subspace-based parameter reduction techniques and discuss strategies
for exploiting such low-dimensional structures - including analysis and computation - to enable
otherwise infeasible parameter studies. For more information, see activesubspaces.org
Department of Applied Mathematics, University of Colorado Boulder
Title
Dispersive hydrodynamics: the mathematics and physics of nonlinear waves in dispersive media
Abstract
Dispersive hydrodynamics - modeled by hyperbolic conservation laws with dispersive perturbation - has emerged as a
unified mathematical framework for the description of multiscale nonlinear wave phenomena in dispersive media and accurately
describes a plethora of physical systems. This talk will be a tour through some recent mathematical and physical
results in this growing field of research. Parallels and analogies to classical hydrodynamics will be
presented such as the generation of shock waves subject to appropriate regularization and their description in
terms of characteristics. From the existence of expansion shocks to the generation of viscous shock waves in
a conservative medium, dispersive regularization also leads to a number of counterintuitive, effects, which will also be described.
