Spatial Interpolation with Message Passing Framework Spatial interpolation is the task to predict a measurement for any location in a given geographical region. To train a prediction model, we assume to have pointwise measurements for various locations in the region. In addition, it is often beneficial to consider historic measurements for these locations when training an interpolation model. Typical use cases are the interpolation of weather, pollution or traffic information. In this paper, we introduce a new type of model with strong relational inductive bias based on Message Passing Networks. In addition, we extend our new model to take geomorphological characteristics into account to improve the prediciton quality. We provide an extensive evaluation based on a large realworld weather dataset and compare our new approach with classical statistical interpolation techniques and Neural Networks without inductive bias.

NearestNeighbor Neural Networks for Geostatistics Kriging is the predominant method used for spatial prediction, but relies on the assumption that predictions are linear combinations of the observations. Kriging often also relies on additional assumptions such as normality and stationarity. We propose a more flexible spatial prediction method based on the NearestNeighbor Neural Network (4N) process that embeds deep learning into a geostatistical model. We show that the 4N process is a valid stochastic process and propose a series of new ways to construct features to be used as inputs to the deep learning model based on neighboring information. Our model framework outperforms some existing stateofart geostatistical modelling methods for simulated nonGaussian data and is applied to a massive forestry dataset.