Dimensionality reduction can be used as a surrogate model for high-dimensional forward uncertainty quantification

• URL: http://arxiv.org/abs/2402.04582v1
• Date: Wed, 7 Feb 2024 04:47:19 GMT
• Title: Dimensionality reduction can be used as a surrogate model for high-dimensional forward uncertainty quantification
• Authors: Jungho Kim, Sang-ri Yi, Ziqi Wang
• Abstract summary: We introduce a method to construct a surrogate model from the results of dimensionality reduction in uncertainty quantification. The proposed approach differs from a sequential application of dimensionality reduction followed by surrogate modeling. The proposed method is demonstrated through two uncertainty quantification problems characterized by high-dimensional input uncertainties.
• Score: 3.218294891039672
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We introduce a method to construct a stochastic surrogate model from the results of dimensionality reduction in forward uncertainty quantification. The hypothesis is that the high-dimensional input augmented by the output of a computational model admits a low-dimensional representation. This assumption can be met by numerous uncertainty quantification applications with physics-based computational models. The proposed approach differs from a sequential application of dimensionality reduction followed by surrogate modeling, as we "extract" a surrogate model from the results of dimensionality reduction in the input-output space. This feature becomes desirable when the input space is genuinely high-dimensional. The proposed method also diverges from the Probabilistic Learning on Manifold, as a reconstruction mapping from the feature space to the input-output space is circumvented. The final product of the proposed method is a stochastic simulator that propagates a deterministic input into a stochastic output, preserving the convenience of a sequential "dimensionality reduction + Gaussian process regression" approach while overcoming some of its limitations. The proposed method is demonstrated through two uncertainty quantification problems characterized by high-dimensional input uncertainties.

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