  Despite the increasingly successful application of neural networks to many
problems in the geosciences, their complex and nonlinear structure makes the
interpretation of their predictions difficult, which limits model trust and
does not allow scientists to gain physical insights about the problem at hand.
Many different methods have been introduced in the emerging field of
eXplainable Artificial Intelligence (XAI), which aim at attributing the
network's prediction to specific features in the input domain. XAI methods are
usually assessed by using benchmark datasets (like MNIST or ImageNet for image
classification), or through deletion/insertion techniques. In either case,
however, an objective, theoretically-derived ground truth for the attribution
is lacking, making the assessment of XAI in many cases subjective. Also,
benchmark datasets for problems in geosciences are rare. Here, we provide a
framework, based on the use of additively separable functions, to generate
attribution benchmark datasets for regression problems for which the ground
truth of the attribution is known a priori. We generate a long benchmark
dataset and train a fully-connected network to learn the underlying function
that was used for simulation. We then compare estimated attribution heatmaps
from different XAI methods to the ground truth in order to identify examples
where specific XAI methods perform well or poorly. We believe that attribution
benchmarks as the ones introduced herein are of great importance for further
application of neural networks in the geosciences, and for accurate
implementation of XAI methods, which will increase model trust and assist in
discovering new science.
