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

TL;DR

This paper presents a novel approach to create stochastic surrogate models for high-dimensional uncertainty quantification by leveraging dimensionality reduction in input-output space, improving efficiency and applicability.

Contribution

The method constructs a surrogate directly from dimensionality reduction results, bypassing the need for sequential modeling and reconstruction, suitable for high-dimensional problems.

Findings

Effective in high-dimensional input scenarios

Preserves input-output relationships accurately

Reduces computational complexity

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.