Mathematics Colloquia and Seminars

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Reduced-order models (ROMs) of nonlinear dynamical systems are

essential for enabling high-fidelity computational models to be used
in many-query and real-time applications such as uncertainty
quantification and design optimization.  Such ROMs reduce the
dimensionality of the dynamical system by executing a projection
process on the governing system of nonlinear ordinary differential
equations.  The resulting ROM can then be numerically integrated in
time.  Unfortunately, many applications require resolving the model
over long time intervals, leading to a large number of time instances
at which the fully discretized model must be resolved.  The number of
time instances required for the ROM simulation remains large, which
can limit its computational savings.

We will go over ROMs for nonlinear dynamical systems.  Especially, a
novel space-time ROM will be introduced.  The model applies space-time
least-squares Petrov-Galerkin projection to decrease both spatial and
temporal complexity.  An error bound with a slow growth rate and
numerical results show its strength and advantage over traditional ROMs.