**4. Conclusion**

*Deep Learning Applications*

weight present lower importance).

that the models developed to predict the density and the speed of sound, the most important variable to determine the kinematic viscosity is the concentration [13]. Finally, from all models developed, both surface tension models were the worst models according to their adjustments. These models are the models with the highest dispersion (RSσ model can be seen in Figure 3.G [13]). The adjustment parameters for all data are low, in fact, the determination coefficient for the RSσ model is around 0.503 (being even lower in the case of ANNσ model −0.451-). Taking into account the AAPD values for all data, it can be seen how neither the RSσ model (14.73%) and the ANNσ model (18.13%) are capable to predict with accuracy the surface tension value. Regarding the input variables, once again, the most impor-

Due to these poor results, the authors [13] proposed an alternative ANN model (ANN'σ) to improve the prediction of surface tension. In this new ANN model, the input variables were increased using the predictions of the ANN models of density, speed of sound and kinematic viscosity, that is, this new ANN model presents an input layer with six variables. The ANN'σ model needs more cycles for its training (12800 cycles) compared to the three input variables ANN model (1200 cycles). It can be shown a notable improvement in the adjustments for the training and the validation phases. The determination coefficient increases to 0.985 for the training phase and 0.940 for the validation phase, while the RMSE values decrease from the 9.6851 mN·m−1 (for all case) to 1.9291 mN·m−1. In the same way, an improvement in the AAPD values is observed, which, in the new model, is below 3.86%. This new model takes the predicted speed of sound as the most important variable, unlike the previous ones, where the most important variable was focused on the concentration. The predicted speed of sound is followed by the predicted kinematic viscosity, the predicted density and the concentration (number of carbons and molecular

Given the results obtained by the surface models and the neural models [13], it can be concluded that the models developed to determine density, sound speed and kinematic viscosity are models suitable for their use in the laboratory due to the low APPD values that presented (between 0.02% and 5.18%, for all the data cases). Regarding the models for surface tension prediction, as previously mentioned, these cannot be used for laboratory use, because they present errors upper than 10%. The alternative ANN model developed by the authors [13], appears to offer acceptable results in terms of determination coefficient and AAPD value. This

All the models developed [13] can be improved in different ways. The response surface models could be improved by adapting the experimental cases to an experimental design before the experimental measurements, allowing on the one hand to save economic costs and time, and on the other, favoring the development of an RS model based on a precise experimental design. It would also be very convenient to develop a response surface model trying to find surfactants that allow the variables to vary constantly in a range. All these improvements could favor the improvement of the models destined to predict the density, the speed of the sound and the

Likewise, and given the ANN model that uses six input variables [13], it would be interesting to develop an RS model that includes the predictions of density, speed of sound and kinematic viscosity as input variables of the model (although it would be necessary to see how to treat the different variation of the values within the range

Neural network models could be improved by including different input variables that are capable of better identification of the different surfactants. Another

interesting approach could by the increase the database for their modeling.

alternative model improves the original RS and ANN model.

tant variable to determine the surface tension is the concentration [13].

**94**

kinematic viscosity.

understudy).

The development of models based on response surfaces and neural networks to predict different physical properties of surfactants aqueous solutions (i) density, ii) speed of sound, iii) kinematic viscosity and iv) surface tension) can be a good alternative to save money and time in the laboratory.

In general terms, this kind of models can adjust, with accuracy, the density, the kinematic viscosity and the speed of sound with determination coefficient upper than 0.902 and lower APPD values than 5.20% (for all data). In contrast to these good adjustments, surface tension models do not work properly and presented (for all data) low determination coefficients (0.503 and 0.451 for RS and ANN model, respectively) and high APPD values (14.73% and 18.13% for RS and ANN model, respectively). It seems that this problem can be solved, in the case of models based on neural networks, with the inclusion of new variables from the predictions of the previous models. With this modification, the new neural model improves (for all data) each adjustment parameter (0.974 and 2.92% for determination coefficient and AAPD value, respectively).

In conclusion, RS and ANN models can be powerful prediction tools for the properties (density, speed of sound, kinematic viscosity or surface tension) of surfactants aqueous solutions. These models could therefore facilitate daily laboratory work, saving time and money. However, it would be interesting to improve the models using other development alternatives or, even, improve these model using different approaches such as support vector machines or random forests, among others.
