In this paper a sparse approximation of inference for multi-output Gaussian Process models based on a Variational Inference approach is presented. In Gaussian Processes a multi-output kernel is a covariance function over correlated outputs. Using a general framework for constructing auto- and cross-covariance functions that are consistent with the physical laws, physical relationships among several outputs can be imposed. One major issue with Gaussian Processes is efficient inference, when scaling up-to large datasets. The issue of scaling becomes even more important when dealing with multiple outputs, since the cost of inference increases rapidly with the number of outputs. In this paper we combine the use of variational inference for efficient inference with multi-output kernels enforcing relationships between outputs. Results of the proposed methodology for synthetic data and real world applications are presented. The main contribution of this paper is the application and validation of our methodology on a dataset of real aircraft flight tests, while imposing knowledge of aircraft physics into the model.
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