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Caleb Magruder
Norbert Wiener Assistant Professor
George McNinch
Contact Info:
Tufts University
Department of Mathematics
503 Boston Avenue
Medford, MA 02155

Email @tufts.edu:

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.


Peer-Reviewed Publications

  • C. Magruder, J. Brandman, H. Denli, "Uncertainty quantification in core flooding," (Submitted to SIAM Journal of Uncertainty Quantification).
  • 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 - 6802.

Other Publications

  • 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, VA, 2012.