Uncertainty Propagation in Deep Gaussian Process Networks

Mathematical Geosciences, vol. 57, pp. 1115–1133

Abstract

Abstract This work presents a deep Gaussian process model for spatial interpolation. The model consists of an irregular network where each node is a Gaussian process whose output is a full Gaussian distribution, as opposed to the single value provided by standard deep neural networks. Each node integrates the uncertainty in its parent nodes analytically through the use of a specialized non-stationary covariance function. The network is capable of modelling multiple variables, even of different types, and its construction allows the imputation of external knowledge, such as lithologically constrained grades and correlations. A special node based on stochastic differential equations learns non-stationary patterns automatically by warping the input space. The model is applied to a time series and two- and three-dimensional cases. An open-source implementation in Python is available.

Authors 2

1. Ítalo Gomes Gonçalves corresponding

   Universidade Federal do Pampa

   Affiliation as printed

   Geological Modeling Laboratory, Federal University of Pampa, Caçapava do Sul, Brazil

2. Florian Wellmann Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany