**4. Discussion**

As can be concluded from Section 3.5, large texture-induced friction reductions, of up to 70%, could already be found experimentally inside the investigated parameter range of textures, velocities, and contact pressures. However, within the physical available samples, it is not always possible to identify clear trends for dimple dimensions that explain a high friction reduction compared to the untextured reference. Based on this finding, it is inferred that the surface texture dimensions need to be individually adapted to the given operating condition, in order to ensure a low friction level.

One possibility to identify optimal surface textures is the examination of a great number of dimple textures, which is significantly larger than the experimentally analysed set. However, this approach would be time-consuming and expensive due to TDM production requirements. The use of additional methods based on AI, such as ROM, are therefore advantageous. In this context, ROM is an effective method for finding the most suitable textures for specific operating conditions, as shown in Section 3.5, where the ROM is used to predict friction reduction values for both experimentally tested and untested working conditions, see Table 5 rows 1–3 and 4, respectively. Within this paper, ROM models have been used to predict and explore friction behaviour of surface textured rubber specimens by training the model on the experimental friction measurement results. Moreover, the model is able to quantify the measured friction variations that occur when deviations from nominal surface texture values are observed (Figures 9, 10a,b, 11a,b and 12a,b). ROM is extremely useful for simulating and predicting a system behaviour, especially when the physics behind its phenomenology are completely unknown or difficult to solve. Thanks to the ROM algorithms, users can predict the behaviour of their system in real-time, and specifically seal manufacturers can assess the parametric conditions that show the desired optimised results and select them before the rubber seal production. The efficiency of a

data-driven ROM, as it is for Twinkle [23], is particularly dependent on the collected data, i.e., their associated error and their resulting manifold coverage.

With a thoroughly planned DoE it is possible to achieve an optimal space coverage, which leads to a reliable ROM's prediction result. The promising results, presented in Section 3.3 for the 2-ROM error propagation (Figure 7) strongly support ROM's accuracy on the given dataset. Nevertheless, if larger amounts of data were available, the computed ROM could be even more reliable in those space regions where less information was collected and, hence, confidently retrieve the best texture that allow minimising friction, according to friction variations computed in Equation (4). Moreover, if a ROM model was computed using simulation data, a higher sample space coverage and hence better reliability in the results could be achieved.

In addition, a ROM model allows verifying that the introduction of a statistical noise on nominal surface texture values affects friction, as shown in Figures 11a,b, where the two-tailed t-Student test showed a statistically significant difference between the experimental friction distribution (orange) and the ideal one (green) for dimple diameterdistance variations, see Figures 12a,b, were the difference on friction measurement are linked to manufacturing deviations in the nominal values of dimple textures. These variations were later compared to the effects obtained from an ideal PDF for dimple values experimental variations, i.e., mean value centred on nominal surface texture values and standard deviation *σ* = 0.01, as shown in Figures 13a,b, opening the way to potential surface texture manufacturing quality and tolerance investigations.
