Deep active subspaces - a scalable method for high-dimensional\n uncertainty propagation

2019/02/27 by Rohit Tripathy, Ilias Bilionis, Tripathy, Rohit +1 · 3 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Decision Sciences · #Advanced Multi-Objective Optimization Algorithms #Cell Image Analysis Techniques #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (stat.ML) #Probabilistic and Robust Engineering Design

paper · pdf · doi:10.48550/arxiv.1902.10527

openalex publication_date 2019/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A problem of considerable importance within the field of uncertainty\nquantification (UQ) is the development of efficient methods for the\nconstruction of accurate surrogate models. Such efforts are particularly\nimportant to applications constrained by high-dimensional uncertain parameter\nspaces. The difficulty of accurate surrogate modeling in such systems, is\nfurther compounded by data scarcity brought about by the large cost of forward\nmodel evaluations. Traditional response surface techniques, such as Gaussian\nprocess regression (or Kriging) and polynomial chaos are difficult to scale to\nhigh dimensions. To make surrogate modeling tractable in expensive\nhigh-dimensional systems, one must resort to dimensionality reduction of the\nstochastic parameter space. A recent dimensionality reduction technique that\nhas shown great promise is the method of `active subspaces'. The classical\nformulation of active subspaces, unfortunately, requires gradient information\nfrom the forward model - often impossible to obtain. In this work, we present a\nsimple, scalable method for recovering active subspaces in high-dimensional\nstochastic systems, without gradient-information that relies on a\nreparameterization of the orthogonal active subspace projection matrix, and\ncouple this formulation with deep neural networks. We demonstrate our approach\non synthetic and real world datasets and show favorable predictive comparison\nto classical active subspaces.\n

Cited by

• Active Subspaces in Infinite Dimension
• Accelerating Hamiltonian Monte Carlo for Bayesian Inference in Neural Networks and Neural Operators
• Structured Neural Chaos: An Adaptive Surrogate Modeling Framework for Functional Uncertainty Quantification and Global Sensitivity Analysis

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