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.

Much of machine learning relies on the use of large amounts of data to train models to make predictions. When this data comes from multiple sources, for example when evaluation of data against a machine learning model is offered as a service, there can be privacy issues and legal concerns over the sharing of data. Fully homomorphic encryption (FHE) allows data to be computed on whilst encrypted, which can provide a solution to the problem of data privacy. However, FHE is both slow and restrictive, so existing algorithms must be manipulated to make them work efficiently under the FHE paradigm. Some commonly used machine learning algorithms, such as Gaussian process regression, are poorly suited to FHE and cannot be manipulated to work both efficiently and accurately. In this paper, we show that a modular approach, which applies FHE to only the sensitive steps of a workflow that need protection, allows one party to make predictions on their data using a Gaussian process regression model built from another party's data, without either party gaining access to the other's data, in a way which is both accurate and efficient. This construction is, to our knowledge, the first example of an effectively encrypted Gaussian process.