**1. Introduction**

Machine Learning (ML) as a subfield of artificial intelligence (AI) has become an integral part of many areas of public life and research in recent years. ML is used to create learning systems that are considerably more powerful than rule-based algorithms and are thus predestined for problems with unclear solution strategies and a high number of variants. ML algorithms are used from product development and production [1] to patient diagnosis and therapy [2]. ML algorithms are also playing an increasingly important role in the field of medical technology, for example, in coatings for joint replacements.

Particularly in coating technology and design, the use of ML algorithms enables the identification of complex relationships between several deposition process parameters on the process itself as well as on the properties of the resulting coatings [3,4]. From this view on the complex relationships between the deposition process parameters, coating designers can base their experiments and obtain valuable insights on their coating designs and the necessary parameter settings for coating deposition.

This contribution looks into the application of a possible ML algorithm in the coating design of amorphous carbon coatings. It first provides an overview of the necessary experimental setup for data generation and the concept of machine learning and its algorithms. Likewise, the deposition of amorphous carbon coatings and their properties are presented. Subsequently, the capabilities of the selected supervised ML algorithms: Polynomial Regression (PR), Support Vector Machines (SVM), Neural Networks (NN), Gaussian Process Regression (GPR) are explained and the resulting data visualization is shown. Afterwards, the obtained results are discussed, with the GPR being the superior

**Citation:** Sauer, C.; Rothammer, B.; Pottin, N.; Bartz, M.; Schleich, B.; Wartzack, S. Design of Amorphous Carbon Coatings Using Gaussian Processes and Advanced Data Visualization. *Lubricants* **2022**, *10*, 22. https://doi.org/10.3390/ lubricants10020022

Received: 14 December 2021 Accepted: 3 February 2022 Published: 7 February 2022

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prediction model. Finally, the main findings are summarized and an outlook is given as well as further potentials and applications are identified.

### **2. Related Work and Main Research Questions**

*2.1. Amorphous Carbon Coating Design*

An example of a complex process is the coating of metal and plastic parts, as used for joint replacements, with amorphous carbon coatings [5]. In the field of machine elements [6,7], engine components [8,9] and tools [10,11], amorphous carbon coatings are commonly used. In contrast, amorphous carbon coatings are rarely used for load-bearing, tribologically stressed implants [12,13]. The coating of engine and machine elements has so far been used with the primary aim of reducing friction, whereas the coating of forming tools has been used to adjust friction while increasing the service life of the tools. Therefore, the application of tribologically effective coating systems on the articulating implant surfaces is a promising approach to reduce wear and friction [14–16].

The coating process depends on many different coating process parameters, such as the bias voltage [17], the target power [18], the gas flow [19] or the temperature, which influence the chemical and mechanical properties as well as the tribological behavior of the resulting coatings [20]. Therefore, it is vital to ensure both the required coating properties and a robust and reproducible coating process to meet the high requirements for medical devices. Compared to experience-based parameter settings, which are often based on trial-and-error, ML algorithms provide clearer and more structured correlations.

However, several experimental investigations focus on improving the tribological effectiveness of joint replacements [21–23] and lubrication conditions in prostheses [24–26], some experimental investigations are complemented with computer-aided or computational methods to improve the prediction and findings [27–29]. Nevertheless, the exact interactions of coating process parameters and resulting properties are mostly qualitative and only valid for certain coating plants and in certain parameter ranges.
