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Abstract

The present work proposes an alternative approach to generate nonlinear reduced order models for optimization and control under uncertainty without explicit knowledge of all the equations governing the physics of the simulation. Hence, the proposed method is amenable for legacy simulation codes. In order to cope with the lack of physical information in conjunction with the inherent curse of dimensionality associated with the number of parameter coefficients, control and state variables of the problem, we combine the projection operators obtained from the Proper Orthogonal Decomposition with neural net interpolation. In this way, the proposed Black-Box Stencil Interpolation Method (BSIM) is capable of exploiting both spatial and temporal variable locality. The method can be seen as a competitive but non-intrusive alternative to the Trajectory Piece-Wise Linear method and the Discrete Empirical Interpolation Method (DEIM) both recently proposed in the literature. We illustrate the capabilities of BSIM on a suite of different black-oil and compositional field models subject to multiple well controls under geological uncertainty. We show that the results are comparable in accuracy to DEIM despite the non-intrusive character of BSIM.

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/content/papers/10.3997/2214-4609.20143193
2012-09-10
2024-03-28
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http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.20143193
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