# Evaluation of Machine Learning Assisted Phase Behavior Modelling of Surfactant-Oil-Water Systems
## 4 Conclusions  
The primary goal of this study was not to demonstrate the superiority or general applicability of machine learning (ML) models in phase behavior modeling, but rather to assess whether highly non-linear and discretized multiphase behavior in surfactant-oil-water systems can be accurately captured, reproduced, and even reasonably near extrapolated using ML approaches. By focusing on complex transitions, including single-phase, two-phase, and three-phase regions, we aimed to test whether ML models can effectively represent these intricate behaviors. The following main conclusions are drawn from this paper:  
1. We tested four machine learning algorithms that demonstrated varying accuracy: fine tree (97.4%), medium tree (93.4%), linear SVM (90.6%), cubic SVM (99.5%), KNN (98.6%), boosted trees (96.9%). The performance of the algorithms was assessed not only based on the accuracy quantification, but also on the overall consistency of phase identification in multiphase regions. The cubic SVM demonstrated the most promising performance in capturing surfactant-oil-water phase behavior.
2. The results show that the cubic SVM was able to successfully reproduce key features of the phase behavior, such as the shrinking of two-phase regions as salinity deviates from optimal conditions, and the model performed well in predicting compositional spaces in near extrapolation.
3. Additionally, this study highlights the robustness and power of the new graphical equation-of-state model, which leverages the compositional space generated by the SVM model or any physical model. The graphical method consistently aligned with both the physical model and experimental data, reinforcing its value as a flexible framework for understanding multiphase behavior in surfactant systems.
4. This hybrid approach, combining ML-generated compositional spaces with a graphical equation-of-state framework, provides a promising avenue for extending the scope of phase behavior modeling while honoring complexity.
5. While machine learning in this context was not intended to replace traditional physical models, it demonstrated the capability to capture and generalize these non-linear transitions, even in near-extrapolated scenarios.  
In conclusion, this work demonstrates that even for highly non-linear systems like surfactant-oil-water mixtures, machine learning combined with novel graphical equation-of-state models are capable of reproducing and generalizing complex phase behavior. While the study did not seek to establish ML as a superior tool over traditional models, it shows that ML can be effectively integrated into phase behavior studies, offering a complementary and powerful way to investigate intricate multiphase phenomena in challenging compositional spaces. Future research may focus on exploring a wider range of machine learning algorithms and their applicability for a chosen system of interest. Moreover, future studies can incorporate experimental data and associated error bars to investigate machine learning application with sparser data and associated uncertainties.  
Conceptualization, D.M. and M.S.; Methodology, D.M. and M.M.; Formal analysis, D.M.; Investigation, D.M.; Resources, M.M. and Z.D.; Writing--original draft, D.M. and M.M.; Supervision, Z.D. and M.S.; Project administration, M.M., Z.D. and M.S.; Funding acquisition, Z.D. and M.S. All authors have read and agreed to the published version of the manuscript.  
This research has been funded by the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan (Grant No. AP13068661).  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare no conflict of interest.