Sobol Tensor Trains for Global Sensitivity Analysis

TL;DR

This paper introduces Sobol Tensor Trains, a novel tensor train-based framework for efficient global sensitivity analysis and surrogate modeling in high-dimensional systems, enabling scalable computation of Sobol indices.

Contribution

The paper presents the Sobol tensor train, a new method for compactly representing all Sobol indices, facilitating efficient sensitivity analysis and variable selection in high-dimensional models.

Findings

Efficient computation of Sobol indices using tensor trains.

Successful application to engineering models and simulation data.

Reduced computational cost for high-dimensional sensitivity analysis.

Abstract

Sobol indices are a widespread quantitative measure for variance-based global sensitivity analysis, but computing and utilizing them remains challenging for high-dimensional systems. We propose the tensor train decomposition (TT) as a unified framework for surrogate modeling and global sensitivity analysis via Sobol indices. We first overview several strategies to build a TT surrogate of the unknown true model using either an adaptive sampling strategy or a predefined set of samples. We then introduce and derive the Sobol tensor train, which compactly represents the Sobol indices for all possible joint variable interactions which are infeasible to compute and store explicitly. Our formulation allows efficient aggregation and subselection operations: we are able to obtain related indices (closed, total, and superset indices) at negligible cost. Furthermore, we exploit an existing global optimization procedure within the TT framework for variable selection and model analysis tasks. We demonstrate our algorithms with two analytical engineering models and a parallel computing simulation data set.