Extreme learning machines for variance-based global sensitivity analysis

TL;DR

This paper introduces sparse weight Extreme Learning Machines (SW-ELMs) as efficient surrogate models for variance-based global sensitivity analysis, enabling analytical Sobol' indices and reducing computational costs.

Contribution

The paper proposes a novel class of SW-ELMs that allow analytical calculation of Sobol' indices, improving accuracy and efficiency in GSA compared to standard ELMs.

Findings

SW-ELMs provide accurate Sobol' index approximations.

The approach reduces computational costs of GSA.

Validated on benchmarks and a chemical reaction network.

Abstract

Variance-based global sensitivity analysis (GSA) can provide a wealth of information when applied to complex models. A well-known Achilles' heel of this approach is its computational cost which often renders it unfeasible in practice. An appealing alternative is to analyze instead the sensitivity of a surrogate model with the goal of lowering computational costs while maintaining sufficient accuracy. Should a surrogate be "simple" enough to be amenable to the analytical calculations of its Sobol' indices, the cost of GSA is essentially reduced to the construction of the surrogate. We propose a new class of sparse weight Extreme Learning Machines (SW-ELMs) which, when considered as surrogates in the context of GSA, admit analytical formulas for their Sobol' indices and, unlike the standard ELMs, yield accurate approximations of these indices. The effectiveness of this approach is illustrated through both traditional benchmarks in the field and on a chemical reaction network.