# Gaussian Process Surrogates for Modeling Uncertainties in a Use Case of Forging Superalloys
## 1 Introduction
We present in the following the main related works to our research field organized in (1) GP regression and FEM simulations, (2) GP regression trained with pure sensor data and (3) optimization with GP regression. In the work of [PERSON] et al. [6], they predict damage development in forged brake discs reinforced with Al-SiC particles using damage maps. In addition to Multilayer Perceptron (MLP), [PERSON] et al. [6] utilize GP regression as a surrogate model. [PERSON] and [PERSON] [7] predict the stress intensity factors using GP regression trained with FEM results of a classical bolt-nut assembly use case. [PERSON] et al. [8] model an electrical discharge machining process with GP regression. [PERSON] et al. [9] utilize GP regression as a surrogate in a structural reliability analysis of a large suspension bridge. In the work of [PERSON] and [PERSON] [10], GP regression is used as a reduced-order model for nonlinear structural analysis in a 1D and 3D use case, where data generation was performed with active learning. [PERSON] et al. [11] use GP regression to estimate residual stresses field of machined parts from two-dimensional numerical simulations. [PERSON] et al. [12] propose two active learning approaches using GP regression for a composite fuselage use case. In the work of [PERSON] et al. [13] GP regression is used as a reduced-order surrogate model for fluid dynamics use cases. [PERSON] et al. [14] use GP regression as a surrogate model of texture in micro-springs. GP regression can also be used on data with multiple fidelity levels, where [PERSON] et al. [15] investigate GP regression surrogate modeling with uncertain material properties of soft tissues and multi-fidelity data. [PERSON] et al. [16] provide an overview of multi-fidelity GP regression techniques in the field of aerospace systems. GP regression can also be extended by methods that stack them or use them in a tree model. [PERSON] et al. [17] predict imperfections in pultruded glass fiber reinforced polymers with a treed method of GP regression trained with experimental data and FEM simulation results. [PERSON] et al. [18] propose a stacked GP regression to integrate different datasets and propagate uncertainties through the stacked model. GP regression can also be used for calibrating simulations, where [PERSON] et al. [19] use GP regression as a surrogate model in a Bayesian model updating method to calibrate FEM simulation of a long-span suspension bridge. In addition to the use of FEM data, GP regression also finds application in the use of pure sensor data, which we will discuss in the following. [PERSON] et al. [20] use a GP regression based surrogate model of a laser powder-bed fusion process to predict melt pool depth. [PERSON] et al. [21] utilize-besides other thriving methods-a GP regression to model the relationship between geological variables and the broken rock zone thickness. [PERSON] [22] uses GP regression trained with experimental data to optimize wire arc additive manufacturing process deposition parameters. [PERSON] et al. [23] propose chained GP regression models based on non-linear latent function combination. [PERSON] et al. [24] provide a heteroskedastic GP regression approach and results of two use cases, namely manufacturing and management of epidemics. In the course of function maximization with GP regression surrogate models, [PERSON] et al. [25] propose a robust optimization approach based on Upper Confidence Bound (UCB) Bayesian Optimization (BO). In another field of optimization, namely solving inverse problems, there is related work found where BO with generalized chi-squared distribution is researched by [PERSON] et al. [26], and [PERSON] and [PERSON] [27], where besides standard GP regression [PERSON] and [PERSON] [27] utilized warped GP regression from the work of [PERSON] et al. [28]. An extension of the standard BO can be found in the work of [PERSON] et al. [29], where they combine BO with the Levenberg-Marquardt method.