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We present a computational framework for dimension reduction and surrogate modeling to accelerate uncertainty quantification in computationally intensive models with high-dimensional inputs and function-valued outputs. Our driving application is multiphase flow in saturated-unsaturated porous media in the context of radioactive waste storage. For fast input dimension reduction, we utilize an approximate global sensitivity measure, for function-valued outputs, motivated by ideas from the active subspace methods. The proposed approach does not require expensive gradient computations. We generate an efficient surrogate model by combining a truncated Karhunen-Loeve (KL) expansion of the output with polynomial chaos expansions, for the output KL modes, constructed in the reduced parameter space. We demonstrate the effectiveness of the proposed surrogate modeling approach with a comprehensive set of numerical experiments, where we consider a number of function-valued (temporally or spatially distributed) QoIs.
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Sensitivity-Driven Adaptive Construction of Reduced-space Surrogates
Surrogate modeling has become a critical component of scientific computing in situationsinvolving expensive model evaluations. However, training a surrogate model can be remark-ably challenging and even computationally prohibitive in the case of intensive simulationsand large-dimensional systems. We develop a systematic approach for surrogate model con-struction in reduced input parameter spaces. A sparse set of model evaluations in the originalinput space is used to approximate derivative based global sensitivity measures (DGSMs)for individual uncertain inputs of the model. An iterative screening procedure is developedthat exploits DGSM estimates in order to identify theunimportantinputs. The screeningprocedure forms an integral part of an overall framework for adaptive construction of a sur-rogate in the reduced space. The framework is tested for computational efficiency throughan initial implementation in simple test cases such as the classic Borehole function, and asemilinear elliptic PDE with a random source function. The framework is then deployed fora realistic application from chemical kinetics, where we study the ignition delay in an H2/O2reaction mechanism with 19 and 33 uncertain rate-controlling parameters. It is observed thatsignificant computational gains can be attained by constructing accurate low-dimensionalsurrogates using the proposed framework.
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- Award ID(s):
- 1745654
- PAR ID:
- 10104991
- Date Published:
- Journal Name:
- Journal of scientific computing
- Volume:
- 79
- ISSN:
- 0885-7474
- Page Range / eLocation ID:
- 1335-1359
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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