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

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.

References in corpus (12)

• Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification
• An active-learning algorithm that combines sparse polynomial chaos expansions and bootstrap for structural reliability analysis
• Polynomial meta-models with canonical low-rank approximations: numerical insights and comparison to sparse polynomial chaos expansions
• Data-driven probability concentration and sampling on manifold
• Uncertainty propagation of p-boxes using sparse polynomial chaos expansions
• Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold
• Manifold learning-based polynomial chaos expansions for high-dimensional surrogate models
• Adaptive active subspace-based metamodeling for high-dimensional reliability analysis
• Language Modeling Is Compression
• A physics and data co-driven surrogate modeling method for high-dimensional rare event simulation
• Optimized Equivalent Linearization for Random Vibration
• Uncertainty quantification for complex systems with very high dimensional response using Grassmann manifold variations