Multiscale method for hazard map construction

This work describes a multiscale approach for creating a fast surrogate of physics based simulators, to improve the speed of applications that requires large ensembles like hazard map creation. The novel framework is applied in determining the probability of the presence of airborne ash at a specific height when an explosive volcanic eruption occurs. The procedure involves representing both the parameter space (sample points at which the numerical model is evaluated) and physical space (ash concentration at a certain height covered by well delimited parcel) by a weighted graph. The combination of graph representation and low rank approximation gives a good approximation of the original graph (allows us to identify a well-conditioned basis of the adjacency matrix for its numerical range) that is less computationally intensive and more accurate when out-of-sample extension is performed at re-sample points as higher resolution parcels.