Scalable sparse co-Kriging for multi-fidelity data fusion: An application to aerodynamics

Multi-fidelity Kriging surrogate modeling combines data of varying accuracy, such as experimental tests and numerical simulations, to improve predictive performance. Autoregressive models are commonly used to capture correlations across fidelity levels, offering interpretability compared to purely data-driven approaches. However, existing frameworks often suffer from high computational costs or rely on restrictive assumptions, such as requiring nested designs of experiments (DoEs). In an engineering context, the latter assumption implies that experimental tests must be conducted at the same input conditions as those used in numerical simulations. This requirement cannot always be met due to safety constraints in tests, which limit flexibility in data acquisition. In this work, we revisit the multi-fidelity Kriging approach and introduce a generalized co-Kriging framework that jointly models multiple fidelity levels through a correlation structure based on the autoregressive model. To ensure scalability, we extend sparse approximation techniques to the multi-fidelity setting, maintaining the efficiency of classical sparse Kriging while improving accuracy. We evaluate our framework on both nested and non-nested DoEs. On a large-scale multi-fidelity aerodynamic dataset that combines wind tunnel experiments with CFD simulations, the percentage of standardized residuals falling outside the confidence intervals is reduced by approximately 75% compared to standard sparse Kriging, highlighting the benefit of incorporating multi-fidelity information in complex engineering applications.