Discovering an active subspace in a single-diode solar cell model
For engineers and scientists running parameter studies on complex models, this method offers a way to reduce dimensionality and computational cost.
The paper introduces a method to detect active subspaces in models and applies it to a five-parameter solar cell model, finding a one-dimensional active subspace that reduces parameter studies from five dimensions to one.
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.