| Description | Nonlinear Model Reduction for Complex Systems
Boris Kramer, Ph.D.
Aerospace Computational Design Laboratory. Department of Aeronautics and Astronautics at Massachusetts Institute of Technology ABSTRACT: Model order reduction for large-scale nonlinear systems is a key enabler for design, uncertainty quantification and control of complex systems. In the first part of the talk, I will discuss a beneficial detour to deriving eÿcient reduced-order models for nonlinear systems. First, the nonlinear model is lifted to a model with more structure via variable transformations and the introduction of auxiliary variables. The lifted model is equivalent to the original model—it uses a change of variables, but introduces no approximations. When discretized, the lifted model yields a polynomial system of either ordinary di˙erential equations or di˙erential algebraic equations, depending on the problem and lifting transformation. Proper orthogonal decomposition (POD) is applied to the lifted models, yielding a reduced-order model for which all reduced-order operators can be pre-computed. We show several examples in form of a FitzHugh-Nagumo PDE and a tubular reactor model, and show how this approach opens new pathways for rigorous analysis and input-independent model reduction via the introduction of the lifted problem structure. In the second part of the talk, I will discuss several applications in uncertainty quantification where reduced-order models are aiding in making existing UQ approaches computationally feasible. E.g., I will discuss conditional-value-at-risk estimation, as well as failure probablity estimation for engineering systems. SPEAKER BIO: Boris Kramer is a Postdoctoral Associate in the Aerospace Computational Design Laboratory (ACDL) at the Massachusetts Institute of Technology, working with Professor Karen Willcox. He earned his Ph.D. (2015) and M.S. (2011) in Mathematics from Virginia Tech, and an under-graduate degree (2009) from the Karlsruhe Institute of Technology, Germany. Boris’ research focuses on computational methods and numerical analysis for control, optimization, design and uncertainty quantification of complex and large-scale dynamical systems. His research revolves around certified reduced-order surrogate modeling with applications in (thermal/reactive) flows. Recent work has been on reliability-based design and design under uncertainty, as well as nonlinear model reduction via state transformations. Boris is an active and passionate member of the Society for Industrial and Applied Mathematics, being recognized for exceptional service as a SIAM Student Chapter president in 2014. |
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