Luca Insolia , Stéphane Guerrier, Chiara Paola Montagna , Maria-Pia Victoria-Feser, Luca Caricchi 

Evolution of volcanic plumbing systems towards eruptions of different styles and sizes largely depends on processes at crustal depths that are outside our observational capabilities. These
processes can be modeled and the outputs of the simulations can be compared with the chemistry of the erupted products, geophysical and geodetic data to retrieve information on the architecture of the plumbing system and the processes leading to eruption. The interaction between magmas with different physical and chemical properties often precedes volcanic eruptions. Thus, sophisticated numerical models have
been developed that describe in detail the dynamics of interacting magmas, specifically aimed at evaluating pre-eruptive magma mingling and mixing timescales. However, our ability to explore the parameters space in order to match petrological and geophysical observations is limited by the extremely high computational costs of these multiphase, multicomponent computational fluid dynamics simulations. To overcome these limitations, we present a statistical emulator that is able to reproduce the numerical simulations results providing the temporal evolution of the distribution of magma chemistry as a function of a set of input parameters such as magma
densities and reservoir shapes. The whole rock composition of volcanic rocks is one of the most
common measurable parameter collected for eruptions. The statistical emulator can be used
to invert the observed distribution of whole rock chemistry to determine the duration of interaction between magmas preceding an eruption and identify the best matching input paramaters of the numerical model. Importantly, the statistical emulator intrinsically includes error propagation, thus providing confidence intervals on predicted interaction timescales on the base of the intrinsic uncertainty of the input parameters of the numerical simulations.