Norbert Wiener Assistant Professor
Department of Mathematics
503 Boston Avenue
Medford, MA 02155
Scientific computing: optimization with partial differential
equations as implicit constraints, model order reduction
My research interests include optimization with implicit constraints
governed by nonlinear partial differential equations and model order
reduction. Applications of my research include science and
engineering problems where physical phenomena are described by
nonlinear partial differential equations, e.g., fluid flows through
porous media and optimal control of chemical reactions.
The computational cost of optimization with partial differential
equations (PDEs) as implicit constraints is driven by solving many
large-scale simulations. This can quickly become prohibitive.
Conventional approaches to model reduction in optimization seek to
approximate the implicit constraint with a reduced order model.
Doing so generates a surrogate model whose solution is considerably
cheaper to compute. Consequently, this reduces the cost of
derivative computations needed for optimization.
However, in my experience with subspace-based model reduction and
optimization, generating reduced order models that are consistently
representative of their original full order models throughout the
optimization is expensive, if not impossible, depending on the
application. My research circumvents these issues by implementing
model reduction in the optimization subproblems instead of replacing
the implicit constraint. The impact of my work is a dramatic speedup
of optimization algorithms where model reduction was previously
unproductive, accelerating these algorithms in increasingly
demanding computational environments.
- C. Magruder, J. Brandman, H. Denli, "Uncertainty
quantification in core flooding," (Submitted to SIAM Journal of
- C. C. Magruder, S. Gugercin, C. A. Beattie, "Linear time-periodic dynamical systems: An H2 analysis and a model reduction framework," Mathematical Modelling of Dynamical Systems, 2017.
- C. Magruder, C.A. Beattie, S. Gugercin, "Rational Krylov
methods for optimal L2 model reduction," Proceedings of the 49th
IEEE Conference on Decision and Control, Atlanta, GA, 2010, pp. 6797
- C. Magruder, "Accelerating Newton's Method for large-scale optimal
control via reduced-order modeling," Ph.D. Thesis, Computational and
Applied Mathematics Department, Rice University, Houston, TX, 2017.
- C. Magruder, "Model reduction of linear time-periodic dynamical
systems," M.S. Thesis, Mathematics Department, Virginia Tech,
Blacksburg, VA, 2013.
- C. Magruder, S. Gugercin, "Model reduction of inhomogeneous
initial conditions," Technical Report, Virginia Tech, Blacksburg,