Multi-fidelity surrogate modelling offers an efficient way to approximate computationally expensive simulations. In particular, Kriging-based surrogate models are popular for approximating deterministic data. In this work, the performance of Kriging is investigated when multi-fidelity gradient data is introduced along with multi-fidelity function data to approximate computationally expensive black-box simulations. To achieve this, the recursive CoKriging formulation is extended by incorporating multi-fidelity gradient information. This approach, denoted by Gradient-Enhanced recursive CoKriging (GECoK), is initially applied to two analytical problems. As expected, results from the analytical benchmark problems show that additional gradient information of different fidelities can significantly improve the accuracy of the Kriging model. Moreover, GECoK provides a better approximation even when the gradient information is only partially available. Further comparison between CoKriging, Gradient Enhanced

The use of surrogate models for approximating computationally expensive simulations has been on the rise for the last two decades. Krigingbased surrogate models are popular for approximating deterministic computer models. In this work, the performance of Kriging is investigated when gradient information is introduced for the approximation of computationally expensive black-box simulations. This approach, known as Gradient Enhanced Kriging, is applied to various benchmark functions of varying dimensionality (2D-20D). As expected, results from the benchmark problems show that additional gradient information can significantly enhance the accuracy of Kriging. Gradient Enhanced Kriging provides a better approximation even when gradient information is only partially available. Further comparison between Gradient Enhanced Kriging and an alternative formulation of Gradient Enhanced Kriging, called indirect Gradient Enhanced Kriging, highlights various advantages of directly employing gradient information, such as improved surrogate model accuracy, better conditioning of the correlation matrix, etc. Finally, Gradient Enhanced Kriging is used to model 6-and 10-variable Fluid-Structure Interaction problems from bio-mechanics to identify the arterial wall's sti↵ness.Keywords Kriging · Surrogate Modelling · Gradient Enhancement · Fluid Structure Interaction S. Ulaganathan · I. Couckuyt · T. Dhaene · E. Laermans Ghent University -iMINDS, Department of Information Technology (INTEC), Gaston Crommenlaan 8, 9050 Ghent, Belgium E-mail: {selvakumar.ulaganathan, ivo.couckuyt, tom.dhaene, eric.laermans}@ugent.be J. Degroote Ghent University, Department of Flow, Heat and Combustion Mechanics, Sint -Pietersnieuwstraat 41, 9000 Ghent, Belgium E-mail: Joris.Degroote@ugent.be 2 S e l v a k u m a r U l a g a n a t h a n e t a l .

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