About this Event
Title:
“Reduced Order Modeling of Finite Time Sensitivities in Evolutionary Systems via Time Dependent Basis Functions”
ABSTRACT:
Enabling reliable computation of finite time sensitivities in evolutionary systems via numerical simulation is a central goal amongst a diverse set of fields and applications. For these systems, sensitivities are a necessary component for understanding the input-output relationship between model inputs and system response across a range of operating conditions. Despite their ubiquity and necessity, state of the art methods for computing sensitivities have a number of fundamental limitations for many applications of interest. These limitations include derivation and implementation of sensitivity equations, computational burden including I/O load, and nonlinear effects for finite perturbations.
The goal of this research is to develop a reduced order modeling framework for computing finite time sensitivities in evolutionary systems. The proposed method is based on a model-driven reduction technique that leverages time dependent basis functions to approximate sensitivities via a low-rank decomposition. The method requires solving forward evolution equations, and does not impose any I/O load. Therefore, it can be used in applications in which real-time sensitivities are of interest. While preliminary work shows the efficacy of the method for computing forward linear sensitivities with a high degree of accuracy, a nonlinear approach is developed to address a number of outstanding challenges with adjoint-based methods and forward linearizations. If this research is successful, we should be able to accurately compute linear and nonlinear sensitivities in evolutionary systems via low-rank approximation.