# Tensor Gaussian Processes (TGP) technique for accuracy evaluation

# Accuracy Evaluation for an approximation in case of factorial Design of Experiments (DoE) can be made using one of pSeven Core GTApprox techniques - Tensor Gaussian Processes. It is another approximation technique designed for factorial Design of Experiments and based on the Gaussian Processes (GP) technique in GTApprox. It is an adaptation of GP technique for factorial DoE. **TGP takes into account the special structure of the training sample**, which makes this technique extremely efficient and accurate.

# TGP technique **features **are:

- handling large training samples with factorial DoE
- accuracy evaluation
- taking into account the features of DoE

Factorization of DoE is often accompanied by DoE's **anisotropy **of various forms:

- the factor sizes can differ significantly;
- the factors can be multidimensional.

GP technique is not flexible enough to provide accurate approximation for such kind of DoE and is able to handle only relatively small samples. TGP technique perfectly fits to solve this problem.

**Accuracy Evaluation for factorial DoE – example**

Let's consider the rotating disc problem as Tensor Gaussian Processes’ application example. In this problem, a disc of an impeller is considered. It is rotated around the shaft. The geometrical shape of the disc considered here is parameterized by 6 variables *h1, h2, h3, h4, r2, r3* . The task is to model maximum radial stress which can be expressed as a function of this 6 variables: *y = f (h1,h2,h3,h4,r2,r3)**. *

The training sample is a factorial DoE. After surrogate model is constructed, we need to assess the quality of approximation. For this purpose, TGP technique is used. It allows to build confidence interval using Accuracy Evaluation (AE) feature.