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Application of POD and DEIM to Dimension Reduction of Nonlinear Miscible Viscous Fingering in Porous Media
A Discrete Empirical Interpolation Method (DEIM) is applied in conjunction with Proper Orthogonal Decomposition (POD) to construct a nonlinear reduced-order model of finite difference discretized system used in the simulation ...
Morphologically Accurate Reduced Order Modeling of Spiking Neurons
Accurately simulating neurons with realistic morphological structure and synaptic inputs requires the solution of large systems of nonlinear ordinary differential equations. We apply model reduction techniques to recover ...
Dimension Reduction for Unsteady Nonlinear Partial Differential Equations via Empirical Interpolation Methods
This thesis evaluates and compares the efficiencies of techniques for constructing reduced-order models for finite difference (FD) and finite element (FE) discretized systems of unsteady nonlinear partial differential ...
Discrete Empirical Interpolation for Nonlinear Model Reduction
A dimension reduction method called Discrete Empirical Interpolation (DEIM) is proposed and shown to dramatically reduce the computational complexity of the popular Proper Orthogonal Decomposition (POD) method for constructing ...