An accurate determination of the catalytic property of thermal protection materials is crucial to design reusable atmospheric entry vehicles. This property is determined by combining experimental measurements and simulations of the reactive boundary layer near the material surface. The inductively-driven Plasmatron facility at the von Karman Institute for Fluid Dynamics provides a test environment to analyze gas-surface interactions under effective hypersonic conditions. In this study, we develop an uncertainty quantification methodology to rebuild values of the gas enthalpy and material catalytic property from Plasmatron experiments. A non-intrusive spectral projection method is coupled with an in-house boundarylayer solver, to propagate uncertainties and provide error bars on the rebuilt gas enthalpy and material catalytic property, as well as to determine which uncertainties have the largest contribution to the outputs of the experiments. We show * Corresponding author. that the uncertainties computed with the methodology developed are significantly reduced compared to those determined using a more conservative engineering approach adopted in the analysis of previous experimental campaigns.

The simulation of complex multi-physics phenomena often relies on a System of Solvers (SoS), which we define here as a set of interdependent solvers where the output of an upstream solver is the input of downstream solvers. Constructing a surrogate model of a SoS presents a clear interest when multiple evaluations of the system are needed, for instance to perform uncertainty quantification and global sensitivity analyses, the resolution of optimization or control problems, and generally any task based on fast query evaluations. In this work, we develop an original mathematical framework, based on Gaussian Process (GP) models, to construct a global surrogate model of the directed SoS, (i.e., only featuring one-way dependencies between solvers). The two central ideas of the proposed approach are, first, to determine a local GP model for each solver constituting the SoS and, second, to define the prediction as the composition of the individual GP models constituting a system of GP models (SoGP). We further propose different adaptive sampling strategies for the construction of the SoGP. These strategies use the decomposition of the SoGP prediction variance into individual contributions of the constitutive GP models and on extensions to SoGP of the Maximum Mean Square Predictive Error criterion. We finally assess the performance of the SoGP framework on several SoS involving different numbers of solvers and structures of input dependencies. The results show that the SoGP framework is very flexible and can handle different types of SoS, with a significantly reduced construction cost (measured by the number of training samples) compared to constructing a unique GP model of the SoS. , systems of solvers have received interest from the community trying to develop efficient UQ methods for SoS. In [11], the authors proposed a method based on importance sampling to decouple the uncertainty propagation process of individual solvers in order to gain flexibility. Other recent works focused on adapting Global Polynomial Chaos (gPC) based methods to SoS, with the challenge of deriving efficient quadrature rules on intermediate inputs with unknown distributions. Using the structure of SoS, the authors of [12] proposed a method for propagating uncertainty in a composite function by adapting the quadrature rule of intermediate inputs in the SoS, thus limiting the number of quadrature points compared to a global black box approach. This work used the recursive formula for orthogonal polynomials and Lanczos algorithms. The same authors generalized this idea in [13] to a full SoS. Their approach relies on Galerkin projection methods at intermediate layers of the SoS. By solving an optimization problem, they proposed a quadrature rule for latent variables, regularized in order to promote sparsity in the weights, thus reducing the number of quadrature points. In [14], the authors tackled the problem of strongly coupled systems. Their main idea is that the dimension of the coupling variables and the amount of information transferred from ...

Quantifying the catalytic properties of reusable thermal protection system materials is essential for the design of atmospheric entry vehicles. Their properties quantify the recombination of oxygen and nitrogen atoms into molecules, and allow for accurate computation of the heat flux to the spacecraft. Their rebuilding from ground test data, however, is not straightforward and subject