Control of the Burgers equation by a reduced-order approach using proper orthogonal decomposition
Journal of Optimization Theory and Applications
Projection frameworks for model reduction of weakly nonlinear systems
Proceedings of the 37th Annual Design Automation Conference
Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics
SIAM Journal on Numerical Analysis
Proceedings of the 2001 IEEE/ACM international conference on Computer-aided design
Journal of Scientific Computing
Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems
Applied Numerical Mathematics
Piecewise polynomial nonlinear model reduction
Proceedings of the 40th annual Design Automation Conference
Linearized reduced-order models for subsurface flow simulation
Journal of Computational Physics
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Proceedings of the 48th Design Automation Conference
ModSpec: an open, flexible specification framework for multi-domain device modelling
Proceedings of the International Conference on Computer-Aided Design
Model order reduction of coupled circuit-device systems
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
SIAM Journal on Scientific Computing
A State Space Error Estimate for POD-DEIM Nonlinear Model Reduction
SIAM Journal on Numerical Analysis
Gradient-enhanced surrogate modeling based on proper orthogonal decomposition
Journal of Computational and Applied Mathematics
A model reduction technique based on the PGD for elastic-viscoplastic computational analysis
Computational Mechanics
POD reduced-order unstructured mesh modeling applied to 2D and 3D fluid flow
Computers & Mathematics with Applications
POD/DEIM nonlinear model order reduction of an ADI implicit shallow water equations model
Journal of Computational Physics
On the optimal control of the Schlögl-model
Computational Optimization and Applications
Mathematics and Computers in Simulation
Two-Step Greedy Algorithm for Reduced Order Quadratures
Journal of Scientific Computing
Model reduction of linear time-varying systems over finite horizons
Applied Numerical Mathematics
A numerical investigation of velocity-pressure reduced order models for incompressible flows
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Non-linear model reduction for the Navier-Stokes equations using residual DEIM method
Journal of Computational Physics
Dynamic Data Driven Application System for Plume Estimation Using UAVs
Journal of Intelligent and Robotic Systems
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A dimension reduction method called discrete empirical interpolation is proposed and shown to dramatically reduce the computational complexity of the popular proper orthogonal decomposition (POD) method for constructing reduced-order models for time dependent and/or parametrized nonlinear partial differential equations (PDEs). In the presence of a general nonlinearity, the standard POD-Galerkin technique reduces dimension in the sense that far fewer variables are present, but the complexity of evaluating the nonlinear term remains that of the original problem. The original empirical interpolation method (EIM) is a modification of POD that reduces the complexity of evaluating the nonlinear term of the reduced model to a cost proportional to the number of reduced variables obtained by POD. We propose a discrete empirical interpolation method (DEIM), a variant that is suitable for reducing the dimension of systems of ordinary differential equations (ODEs) of a certain type. As presented here, it is applicable to ODEs arising from finite difference discretization of time dependent PDEs and/or parametrically dependent steady state problems. However, the approach extends to arbitrary systems of nonlinear ODEs with minor modification. Our contribution is a greatly simplified description of the EIM in a finite-dimensional setting that possesses an error bound on the quality of approximation. An application of DEIM to a finite difference discretization of the one-dimensional FitzHugh-Nagumo equations is shown to reduce the dimension from 1024 to order 5 variables with negligible error over a long-time integration that fully captures nonlinear limit cycle behavior. We also demonstrate applicability in higher spatial dimensions with similar state space dimension reduction and accuracy results.