## 1 Introduction  
Over the past few decades, surrogate modelling or so-called meta-modelling has increasingly been employed for predicting results of physical computer simulations. Simulations can become prohibitively expensive when multiple realizations are required, as is the case with Uncertainty Quantification (UQ) or optimisation processes; the fast evaluation speed of surrogates makes them an attractive alternative, and have led to their wide acceptance and adoption in several engineering fields (see [1] for an overview of UQ with surrogate strategies). In the case of aerospace engineering design problems, where the failure allowance is quite limited, uncertainties for the design space variables are propagated through the output and have to be estimated accurately without any loss of reliability and within a reasonable period of time. In uncertainty quantification processes, even using surrogates for approximating physical phenomena can be quite time consuming and costly due to the need for many high-fidelity simulations to achieve reliable and robust designs, especially in the case of high-dimensional design optimisation problems. Thus, in an effort to further alleviate the computational burden of UQ, single-fidelity surrogates are extended to multi-fidelity versions by using additive and multiplicative correction approaches to reach an acceptable accuracy in limited time. Multi-fidelity models use different fidelity levels, which may significantly reduce the computational load and accelerate the computation. These models have been widely used to overcome the computational burden in uncertainty modelling and optimisation processes for complex simulations. The key feature behind the multi-fidelity methodology is to increase the accuracy of the intensively sampled low-fidelity simulations by exploiting a limited number of high-fidelity simulations, thus maintaining an acceptable computational cost. A comprehensive review for multi-fidelity methods in uncertainty quantification can be found in [2]. The main challenge in simulation-based realisations of engineering problems is the outgrowth in dimensionality, which increases the complexity and the computational time for calculating hyperparameters of the implemented surrogate. Particularly as dimensionality grows large, the Low-Rank Approximation (LRA) methodology is a prominent tool among surrogate modelling strategies model strategies, since the method models the response of the system as the sum of a smaller number of rank-one tensors, which are products of univariate functions. Since approximating the system of outputs is conducted using a smaller number of rank tensors, the number of unknown coefficients to be calculated grows only linearly with the input dimensions, which makes the method very advantageous, especially in high-dimensional cases. The LRA method has been applied to several engineering disciplines recently, with particular focus on scaling with dimensionality; these topics include reliability-based optimisation [3; 4; 5], surrogate model strategies [6; 7], uncertainty propagation [8; 9; 10], sensitivity analysis [11] and comparative studies with the Polynomial Chaos Expansion (PCE) method [12]. LRA is proposed as an alternative surrogate technique to the widely applied PCE. The number of unknown coefficients grows exponentially with the input size in the PCE method, whereas LRA has the advantage of only linearly increasing the number of coefficients with input size. In this study, LRA is therefore selected as a promising surrogate modelling method to overcome the burden of dimensionality as an alternative to PCE. A number of related studies have been carried out in the literature. For instance, [PERSON] and [PERSON] [13] focused on uncertainty quantification and sensitivity analysis for high-dimensional problems; in particular, they calculated design variable sensitivities for different sizes of problems with the surrogate model using the Sparse Polynomial Chaos Expansion (SPCE) method.