## MODEL REDUCTION FOR LARGE-SCALE SYSTEMS WITH HIGH-DIMENSIONAL PARAMETRIC INPUT SPACE (2007)

Citations: | 11 - 2 self |

### BibTeX

@MISC{Bui-thanh07modelreduction,

author = {T. Bui-thanh and K. Willcox and O. Ghattas},

title = {MODEL REDUCTION FOR LARGE-SCALE SYSTEMS WITH HIGH-DIMENSIONAL PARAMETRIC INPUT SPACE},

year = {2007}

}

### OpenURL

### Abstract

Abstract. 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 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 for 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 this example, 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.

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Citation Context ...l, the results also hold for the optimization problem (3.9)–(3.12). We further note that we could use other criteria in the objective function, such as those stemming from optimal experimental design =-=[20]-=-, provided the formulation is tractable for large-scale systems, such as those arising from discretization of PDEs. 3.3. Greedy adaptive sampling via model-constrained optimization. The model-constrai... |

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Citation Context ...n (CVT) sampling method [11] has been shown to outperform LHS, random sampling Monte Carlo methods, and Hammersley quasi Monte Carlo sequence methods for statistical sampling and function integration =-=[26]-=-. To address the challenge of sampling a high-dimensional parameter space to build a reduced basis, the greedy sampling method was introduced in [14,15,31,32]. The key premise of greedy sampling is to... |

1 |
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Citation Context ...or Krylov basis for problems in which the number of input parameters is small, for example aerodynamic applications [13], Rayleigh-Bénard convection [21], parametrized design of interconnect circuits =-=[5, 10]-=-, and parameters describing inhomogeneous boundary conditions for parabolic PDEs [17]. For optimal control applications, online adaptive sampling has been employed as a systematic way to generate snap... |

1 |
Initial evaluation of REDUCTION FOR PARAMETRIC INPUT SPACES 19 pure and latinized centroidal Voronoi tessellation for non-uniform statistical sampling
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(Show Context)
Citation Context ...n (CVT) sampling method [11] has been shown to outperform LHS, random sampling Monte Carlo methods, and Hammersley quasi Monte Carlo sequence methods for statistical sampling and function integration =-=[25]-=-. To address the challenge of sampling a high-dimensional parameter space to build a reduced basis, the greedy sampling method was introduced in [14,15,30,31]. The key premise of greedy sampling is to... |