Discovering an active subspace in a single-diode solar cell model

TL;DR

This paper demonstrates how identifying an active subspace in a solar cell model reduces the complexity of parameter studies from five dimensions to one, improving efficiency in predictions and analysis.

Contribution

The paper introduces a method to verify the presence of an active subspace and applies it to a solar cell model, revealing a dominant one-dimensional subspace.

Findings

The solar cell's maximum power has a dominant one-dimensional active subspace.

Parameter studies can be simplified from five to one dimension.

The method effectively identifies important input directions.

Abstract

Predictions from science and engineering models depend on the values of the model's input parameters. As the number of parameters increases, algorithmic parameter studies like optimization or uncertainty quantification require many more model evaluations. One way to combat this curse of dimensionality is to seek an alternative parameterization with fewer variables that produces comparable predictions. The active subspace is a low-dimensional linear subspace defined by important directions in the model's input space; input perturbations along these directions change the model's prediction more, on average, than perturbations orthogonal to the important directions. We describe a method for checking if a model admits an exploitable active subspace, and we apply this method to a single-diode solar cell model with five input parameters. We find that the maximum power of the solar cell has a dominant one-dimensional active subspace, which enables us to perform thorough parameter studies in one dimension instead of five.