*Article* **Design of Amorphous Carbon Coatings Using Gaussian Processes and Advanced Data Visualization**

**Christopher Sauer \*, Benedict Rothammer, Nicolai Pottin, Marcel Bartz, Benjamin Schleich and Sandro Wartzack**

Engineering Design, Friedrich-Alexander-Universität Erlangen-Nürnberg, Martensstraße 9, 91058 Erlangen, Germany; rothammer@mfk.fau.de (B.R.); nicolai.pottin@fau.de (N.P.); bartz@mfk.fau.de (M.B.); schleich@mfk.fau.de (B.S.); wartzack@mfk.fau.de (S.W.)

**\*** Correspondence: sauer@mfk.fau.de

**Abstract:** In recent years, an increasing number of machine learning applications in tribology and coating design have been reported. Motivated by this, this contribution highlights the use of Gaussian processes for the prediction of the resulting coating characteristics to enhance the design of amorphous carbon coatings. In this regard, by using Gaussian process regression (GPR) models, a visualization of the process map of available coating design is created. The training of the GPR models is based on the experimental results of a centrally composed full factorial 2<sup>3</sup> experimental design for the deposition of a-C:H coatings on medical UHMWPE. In addition, different supervised machine learning (ML) models, such as Polynomial Regression (PR), Support Vector Machines (SVM) and Neural Networks (NN) are trained. All models are then used to predict the resulting indentation hardness of a complete statistical experimental design using the Box–Behnken design. The results are finally compared, with the GPR being of superior performance. The performance of the overall approach, in terms of quality and quantity of predictions as well as in terms of usage in visualization, is demonstrated using an initial dataset of 10 characterized amorphous carbon coatings on UHMWPE.

**Keywords:** machine learning; amorphous carbon coatings; UHWMPE; total knee replacement; Gaussian processes
