Applied Math Seminar: Optimization Under Uncertainty For Atmospheric Trace Gas Transport
Event Type:
Seminar
Speaker:
Bart van Bloemen Waanders, SNL
Event Date:
Monday, November 21, 2016 - 3:30pm
Location:
SMLC 356
Sponsor/s:
Deborah Sulsky
Event Description:
We present an approach to solve control problems under uncertainty by
augmenting the objective function with pre-established performance
criteria. This is accomplished through the risk measure concepts used
in stochastic optimization to manage risk in the financial community.
Recently, risk measures have been applied to engineering optimization
problems constrained by partial differential equations and in this
work we adopt similar strategies to control of anthropogenic CO2
sources with uncertainties in biospheric sources. An inverse problem
is typically a prerequisite before solving the control problem in
order to calibrate coefficients of the underlying dynamics against
field data or experimental measurements. The connection to risk
measures in the context of inverse problems is discussed equating the
risk neutral measure to a maximum posteriori estimate in the linear
and Gaussian case. A mapping of the uncertainty from the inverse to
the control problem is demonstrated on atmospheric trace-gas transport
dynamics. Specifically, control strategies of trace-gas source terms
on an emulated global model are solved to achieve temporal and spatial
targets and account for uncertainty arising from different aspects of
the dynamics.
An important aspect of solving the control under uncertainty problem
is the development of a software framework that can enables large
scale optimization with partial differential equation constraints.
The optimization problem can contain millions of design parameters in
addition to many uncertainties. To that end, we leverage several
components from the Trilinos framework. In particular, the Rapid
Optimization Library (ROL) provides Newton-based optimization, line
search, trust region, and stochastic optimization algorithms. ROL
enables special interfaces that carefully map the underlying linear
algebra of the simulation software to function space requirements for
optimization. Furthermore, to approximate disparate PDE constraints, a
finite element framework has been developed that leverages other
Trilinos packages and automates discretizations, adjoints, and the
optimization interfaces to ROL.
Refreshments will be served in the lounge at 3:00.
