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Acknowledgments Firstly, the work would not have been possible without the guidance of Professor Dar-mofal and the generous funding provided by NASA Langley (grant number NAG1-03035). Secondly, the effort put into Project X by faculty and students (past and present) have made it possible to carry out the computational demonstrations in higher-order DG. In(More)
SUMMARY Model reduction has significant potential in design, optimization and probabilistic analysis applications, but including the parameter dependence in the reduced-order model (ROM) remains challenging. In this work, interpolation among reduced-order matrices is proposed as a means to obtain parameterized ROMs. These ROMs are fast to evaluate and(More)
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract. This paper presents a new approach to construct more efficient(More)
Surrogate-based-optimization methods provide a means to minimize expensive high-fidelity models at reduced computational cost. The methods are useful in problems for which two models of the same physical system exist: a high-fidelity model which is accurate and expensive, and a low-fidelity model which is less costly but less accurate. A number of model(More)
A model-constrained adaptive sampling methodology is proposed for 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(More)
SUMMARY We present a model reduction approach to the solution of large-scale statistical inverse problems in a Bayesian inference setting. A key to the model reduction is an efficient representation of the non-linear terms in the reduced model. To achieve this, we present a formulation that employs masked projection of the discrete equations; that is, we(More)
A greedy algorithm for the construction of a reduced model with reduction in both parameter and state is developed for efficient solution of statistical inverse problems governed by partial differential equations with distributed parameters. Large-scale models are too costly to evaluate repeatedly, as is required in the statistical setting. Furthermore,(More)
— In this paper we present a methodology for achieving real-time control of systems modeled by partial differential equations. The methodology uses the explicit solution of the model predictive control (MPC) problem combined with model reduction. The explicit solution of the MPC problem leads to on-line MPC functionality without having to solve an(More)