- Principal Member of the Technical Staff
- Sandia National Laboratories – Livermore, CA
I am a Principal Member of the Technical Staff in the Quantitative Modeling and Analysis Department
at Sandia National Laboratories in Livermore, CA. Prior to joining Sandia in 1998, I was Chief of the Applied and Computational Mathematics Division at the National Institute of Standards and Technology in Gaithersburg, MD. My resarch interests include nonlinear optimization, in particular the solution of nonlinear problems constrained by partial differential equations. Recently, I have been working on multiscale, multiphysics problems that exhibit hierarchical structure and have developed multigrid optimization and domain decomposition algorithms for their solution. My research interests also include uncertainty quantification based on Bayesian techniques.
Research Projects
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Optimization Algorithms for Hierarchical Problems, with Application to Nanoporous Materials
The goal of the project is the optimal design of nanoporous materials for the efficient storage of gas and/or electric charge. Since capacity and rapid utilization are both important, the optimization project is to construct the material in such a manner that allows maximum possible energy discharge from a system of fixed volume within a specified discharge period. This generally requires construction of a hierarchical network having an optimal balance between nanoscale pores, which provide high surface area, and transport channels for charging and discharging. To this end we developed a novel mathematical description wherein transport channels coincide with boundaries of finite elements containing nanoscale porosity. For computational efficiency, we identified surrogate steady-state flow problems having nearly the same optima and we developed a multilevel optimization algorithm framework for the solution of such hierarchical problems where the physics changes fundamentally from the nano to the macro scale.
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Optimal Control of Open Quantum Systems
Quantum computing and, more generally, quantum information science, offers
the possibility of exponential increases in computing speed for certain
classes of computations. Such advances can and will have a dramatic effect
on national security. One of the major obstacles in reaching these goals is
the ability to control quantum systems that are in contact with an
incompletely known environment, so-called open quantum systems. The goal of
this project is to develop models for the optimal control of open systems in
order to assess the extent to which effective and robust control can be
applied.
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Calculating Reliability and Optimal Testing Strategies for Hierarchical Systems
The goal of this project is to predict the reliability of a complex,
hierarchical system, but, more importantly, we also want to compute our
confidence in that estimate. The system is described by a tree network,
representing the fact that we are dealing with a "system of systems."
The prediction is done from test data that has
been acquired at various points (nodes) in the network. We use polynomial
chaos expansions to represent the unknown random variables at the leaf
nodes and Bayes' Theorem to propagate the information through the system. The
result is a distribution of the reliability from which many questions,
including confidence, can be posed. We have extended this work to
time-dependent systems so that ageing effects can be studied. Finally, we
have developed a framework in which we can pose optimal testing questions,
including where to test next to obtain the greatest improvement in confidence.
Recent Publications:
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Paul T. Boggs, David M. Gay, Stewart K. Griffiths, Robert Michael Lewis,
Kevin R. Long, Stephen G. Nash, and Robert H. Nilson.
Optimization algorithms for hierarchical problems, with application
to nanoporous materials.
SIAM Journal on Optimization, In review.
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Kevin R. Long, Bart van Bloemen Waanders, and Paul T.
Boggs.
Sundance: High-level software for pde-constrained optimization. Scientific Computing, to appear, 2012.
- Paul T. Boggs, David M. Gay, and Robert H. Nilson.
Network heuristics for initial guesses to nanoporous flow
optimization problems.
Sand report, Sandia National Laboratories, 2012.
- K. T. Carlberg, Ray S. Tuminaro, and Paul T. Boggs.
Efficient structure-preserving model reduction for nonlinear
mechanical systems with application to structural dynamics.
In Proceedings of the Conference on Aeronautics and
Astronautics, 2012.
- P. T. Boggs, M. D. Grace, P. P. Pébay, and J. T. Ringland.
Determining the Bayesian optimal sampling strategy in a
hierarchical system.
Technical Report SAND2010-6661, Sandia National Laboratories, 2010.
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Paul T. Boggs