## 2 Materials and Methods  
### Experimental Setup Description  
A set of experiments was conducted where the temperature was measured in a nickel super alloy material (Inconel 718). To obtain the most efficient results in terms of temperature field in the specimen, the input parameters of the process were defined in correlation with the measured temperature of the material. A sufficiently large sample of experimental data was presented as the basis for designing the machine learning-based model. Liquefied nitrogen was applied on the Inconel 718 plate with the following dimensions: 250 \(\times\) 146 \(\times\) 2.5 mm. The plate was polished at \(R_{a}\) < 0.3 um on the upper side where the flow of the media was applied. On the bottom side of the plate, 3 sets of 5 holes within 5 mm distance were manufactured by EDM or electrical discharge machining (Figure 1). Each set of holes was at the same depth. The nozzle (internal diameter \(d_{\mathrm{n}}\) = 1 mm) was clamped on the magnetic holder on the spindle of the Computer numerical controlled (CNC) machine and moved across the middle of the plate, right above the middle hole set on the polished surface of the plate. The nozzle was moved across the middle of the plate, right above the middle hole on the grinded surface of the plate. In the experiments, five commercial thermocouples Ni Cr-Ni (K-type, diameter 1 mm, insulated, \(T_{\mathrm{t}}\) = -200 to 205 \({}^{\circ}\)C) were used. The thermocouples were fixed to the holes with a power tape. To assure contact of the thermocouple with the workpiece, a thermo paste based on silicon oil with metal oxides was used. The nozzle diameter was 1 mm and moved 15 mm above the plate. Figure 1: Schematic illustration of the moving nozzle with corresponding positions of the thermocouples and a cross section view of the holes at different depths [10]. Liquefied nitrogen was piped through the nozzle under pressure measured on the liquefied nitrogen dewar \(p=1.8\times 10^{5}\) Pa.  
For data acquisition, National instruments (NI) acquisition card was used. The input parameters were determined and with them the design of the experiments. The temperature of the material \(T\) [\({}^{\circ}\)C] was measured, depending on the changing of the input parameters: velocity of the nozzle \(v\), depth of the measuring temperature \(d\) and distance from the moving nozzle \(x\). The value range for the moving nozzle speed \(v\) was defined based on the comparable cutting speed recommended for machining Inconel 718. By the determination of the values, the aim was to determine the temperature drop in the material after the nozzle had moved across the plate. This was compared to one workpiece revolution in the turning process or milling process. The design of the experiments consisted of 35 experiments at different nozzle moving speeds \(v\) = (5, 15, 25, 35 m/min), at different depths at which the temperature in the material was measured \(d\) = (0.1, 0.5, 1 mm), and at different plate-nozzle distances \(x\) = (0, 5, 10 mm). Figure 2 shows the experimental setup (the clamping of the nozzle onto the machine spindle and the detail that shows the diameter of the jet dispersion on the surface) [10]. Table 1 shows the results obtained by measuring the temperatures in the Inconel 718 cooled by the liquefied nitrogen. It can be deduced that the temperature drop in the material significantly decreased with the increasing nozzle speed and this had a greater impact on its cooling ability. Figure 2: Experimental setup [10]. Figure 3 shows an experiment on the measured temperature-time distribution for a moving speed of \(v\) = 5 m/min. Five temperature-time curves for each thermocouple were positioned at the same depth (\(d\) = 0.5 mm) to provide enough information for describing the temperature field in the plate with the aim of obtaining the most efficient empirical model with neural networks. The process