<p>Artificial neural networks (ANN), which are mainly used in pattern and image recognition, have now found a wide range of applications in soil science and geoscience. They have proven to be a useful tool for complex questions that also involve a large amount of data, for example prediction of soil classes or soil properties on various scales. However, we face two main challenges when applying ANN: In their basic form, deep-learning algorithms do not provide interpretable predictive uncertainty. Thus, in geosciences and in particular in soil science, they have been used more as black-box models and properties of a machine learning model such as the certainty and plausibility of the predicted variables, for example soil classes, were interpretation by experts rather than quantified by metrics validating the ANN. In most cases regression coefficients or comparable statistical measure are reported for the overall performance of the model. This leads to the second challenge, that is that these algorithms have high confidence of their predictions in areas far away from the training area or in areas where they receive only little information from a small number of data points. <br />In order to gain a better understanding of these aforementioned properties, we implement in our explorative study on soil classification a Bayesian deep learning approach (i.e., a method to add uncertainty to deep networks) known as last layer Laplace approximation. This is a technique that can be applied as a post-hoc "add-on" without destroying the otherwise good performance of deep classifiers. It helps us to correct the overconfident areas without reducing the accuracy of our prediction, giving us a more realistic uncertainty expression of the model's prediction.  <br />Our predictor variable soil type provides us with a large amount of complex information about soil processes and properties, which is a great advantage since it would take a lot of time and money to collect all this information individually. At the same time, soil maps are in high demand by authorities, construction companies or farmers. In our study area around Tübingen in southern Germany, there are 41 different soil types, determined according to the German soil classification, sub divisible into typical soils of the Neckar and Ammer valleys, the Swabian Jura and Black Forest, and non-area related soil. In addition to the underlying soil map, remotely sensed variables, a digital elevation model and its derivatives are used as input to the ANN, which is designed to learn the relationship between these and the soil type. As a test case, we then explicitly exclude the Swabian Jura and Black Forest in the training area but include them as prediction regions. Both regions are characterized by very different soil types compared to the rest of the study area due to their considerably different geology, climate, and terrain. Our goal is then to enrich soil type maps with a structured uncertainty to better understand the causality of machine learning models in soil science and their transferability to regions other than the training and validation area.</p>

<p>Artificial neural networks (ANN), which are mainly used in pattern and image recognition, have now found a wide range of applications. In recent years, different variants of ANN have also been increasingly used in the geosciences. They have proven to be a useful tool for complex questions that also involve a large amount of data. In their basic form, however, deep-learning algorithms do not provide interpretable predictive uncertainty. In the geosciences in particular, they have been used more as black-box models that require interpretation by an expert or do not allow for specific interpretation. Therefore, we implement in our explorative study on soil classification a Bayesian deep learning approach (i.e. a method to add uncertainty to deep networks) known as last layer Laplace approximation. This is a technique that can be applied as a post-hoc "add-on" without destroying the otherwise good performance of deep classifiers. <br>Our target soil type variable provides us with a large amount of information about soil processes and properties, which is a great advantage since it would take a lot of time and money to collect all this information individually. At the same time, soil maps are in high demand by authorities, construction companies or farmers. In our study area around Tübingen in southern Germany, there are 39 different soil types, determined according to the German soil systematics, which we consider individually for the prediction, but also combine into superordinate categories with similar properties, which is possible at low computational cost under the Laplace approximation. In addition to the underlying soil map, remotely sensed variables such as satellite imagery, a digital elevation model and its derivatives, and climate data are used as input to the model, which is designed to learn the relationship between these and the soil type.  As a test case, we then explicitly include the Swabian Jura as a prediction region for the environment. This region is characterised by very different soil types due to its extremely different development and the resulting geology, climate and terrain. <br>Our goal is then to enrich soil type maps with a structured uncertainty, which is estimated to be high in the area of the Swabian Jura. This will help to better understand the causality of machine learning models in soil science and their transferability to regions other than the training and validation area.</p>

<p>The goal of this work is to perform soil classification with uncertainty quantification for a structured treatment of the output classes. Uncertainty can help in this setting to make predictions more informative with regard to class relationships. This is of particular interest due to the often highly related nature of the distinguished soil types. Incorporating knowledge about class structure into the model also provides opportunity for improving the model accuracy. Our main focus, however, is to enable modellers to better understand and work with this structure during analysis.<br>For example, post-hoc aggregation of class labels into supersets facilitates applications such as letting the model choose an ontological level on which it can confidently distinguish the output class. It can likewise be used to determine the combined probability of specified classes that share a property of interest.<br>Technically, this works by learning a latent Gaussian distribution, for example using a Gaussian Process model, and mapping it to a distribution over the class probabilities. We demonstrate this approach, explore possible applications for exploiting uncertainty information, in particular with regard to the class hierarchy, and compare the performance of different model variants in terms of accuracy and calibration.</p>