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The ever-increasing capability of computational methods has resulted in their general acceptance as a key part of the materials design process. Traditionally this has been achieved using a so-called computational funnel, where increasingly accurate - and expensive – methodologies are used to winnow down a large initial library to a size which can be tackled by experiment. In this paper we present an alternative approach, using a multi-output Gaussian process to fuse the information gained from both experimental and computational methods into a single, dynamically evolving design. Common challenges with computational funnels, such as mis-ordering methods, and the inclusion of non-informative steps are avoided by learning the relationships between methods on the fly. We show this approach reduces overall optimisation cost on average by around a factor of three compared to other commonly used approaches, through evaluation on three challenging materials design problems. [ABSTRACT FROM AUTHOR]