Forecasting volcanic plume hazards with fast UQ

This paper introduces a numerically-stable multiscale scheme to efficiently generate probabilistic hazard maps for volcanic ash transport using models of transport, dispersion and wind. The scheme relies on graph-based algorithms and low-rank approximations of the adjacency matrix of the graph. This procedure involves representing both the parameter space and physical space by a weighted graph. A combination of clustering and low rank approximation is then used to create a good approximation of the original graph. By performing a multiscale data sampling, a well-conditioned basis of a low rank Gaussian kernel matrix, is identified and used for out-of-sample extensions used in generating the hazard maps.