*3.1. Numerical Fitting of the Pseudo-Experimental Data Set*

Recalling Section 2.3, Figure 5 shows the "mean" GENERIC model when compared to the noise-free numerical experiment.

**Figure 5.** Comparison of (**a**) horizontal and (**b**) vertical displacement predicted by a General Equation for the Nonequilibrium Reversible-Irreversible Coupling (GENERIC) model obtained as the mean of 50 different noisy GENERIC models. Comparison with the noise-free reference solution in continuous blue line.

As can be noticed from this figure, results show a poor accordance to the noise-free version of the data. Constructing a model by just computing the mean of each GENERIC model for noisy data seems not to be a good idea. If we consider it here, it is just because in the experimental framework, phenomenological models are very often obtained after computing means of the available results [14].

Figure 6 shows a displacement comparison among the noise-free sample and the full GENERIC-TDA model with different Kriging interpolation techniques. Additionally, Table 1 shows the obtained 2-norm errors of the mentioned model results.

(**b**) Vertical displacement

**Figure 6.** Comparison of (**a**) horizontal and (**b**) vertical displacement predicted by a GENERIC model obtained as the mean of 50 different noisy GENERIC models. Comparison with the noise-free reference solution in continuous blue line and the solutions obtained by Kriging interpolation between neighbors predicted by Topological Data Analysis.

**Table 1.** 2-norm errors in the obtention of the GENERIC model.


It is worth noting the high degree of accuracy obtained by employing local Kriging procedures. In combination with TDA, this procedure is able not just to filter the artificial noise added to the data, but to provide a very accurate GENERIC model able to reproduce the visco-hyperelastic model from which pseudo-experimental data was obtained.
