Model reduction for large-scale dynamical systems via equality constrained least squares
Journal of Computational and Applied Mathematics
Variation-aware interconnect extraction using statistical moment preserving model order reduction
Proceedings of the Conference on Design, Automation and Test in Europe
A Framework for Reduced Order Modeling with Mixed Moment Matching and Peak Error Objectives
SIAM Journal on Scientific Computing
On Adaptive Choice of Shifts in Rational Krylov Subspace Reduction of Evolutionary Problems
SIAM Journal on Scientific Computing
Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems
SIAM Journal on Scientific Computing
Interpolatory Projection Methods for Parameterized Model Reduction
SIAM Journal on Scientific Computing
Journal of Scientific Computing
Simulation-based optimal Bayesian experimental design for nonlinear systems
Journal of Computational Physics
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A model-constrained adaptive sampling methodology is proposed for the reduction of large-scale systems with high-dimensional parametric input spaces. Our model reduction method uses a reduced basis approach, which requires the computation of high-fidelity solutions at a number of sample points throughout the parametric input space. A key challenge that must be addressed in the optimization, control, and probabilistic settings is the need for the reduced models to capture variation over this parametric input space, which, for many applications, will be of high dimension. We pose the task of determining appropriate sample points as a PDE-constrained optimization problem, which is implemented using an efficient adaptive algorithm that scales well to systems with a large number of parameters. The methodology is demonstrated using examples with parametric input spaces of dimension 11 and 21, which describe thermal analysis and design of a heat conduction fin, and compared with statistically based sampling methods. For these examples, the model-constrained adaptive sampling leads to reduced models that, for a given basis size, have error several orders of magnitude smaller than that obtained using the other methods.