Fast Prediction of the Equivalent Alkane Carbon Number Using Graph Machines and Neural Networks

The hydrophobicity of oils is a key parameter to design surfactant/oil/water (SOW) macro-, micro-, or nano-dispersed systems with the desired features. This essential physicochemical characteristic is quantitatively expressed by the equivalent alkane carbon number (EACN) whose experimental determination is tedious since it requires knowledge of the phase behavior of the SOW systems at different temperatures and for different surfactant concentrations. In this work, two mathematical models are proposed for the rapid prediction of the EACN of oils. They have been designed using artificial intelligence (machine-learning) methods, namely, neural networks (NN) and graph machines (GM). While the GM model is implemented from the SMILES codes of a 111-molecule training set of known EACN values, the NN model is fed with some σ-moment descriptors computed with the COSMOtherm software for the 111-molecule set. In a preliminary step, the leave-one-out algorithm is used to select, given the available data, the appropriate complexity of the two models. A comparison of the EACNs of liquids of a fresh set of 10 complex cosmetic and perfumery molecules shows that the two approaches provide comparable results in terms of accuracy and reliability. Finally, the NN and GM models are applied to nine series of homologous compounds, for which the GM model results are in better agreement with the experimental EACN trends than the NN model predictions. The results obtained by the GMs and by the NN based on σ-moments can be duplicated with the demonstration tool available for download as detailed in the Supporting Information.油的疏水性是设计具备预期特性的表面活性剂/油/水（SOW）宏观、微观或纳米分散体系的关键参数。这一重要的物理化学特征可通过等效烷烃碳数（EACN）进行定量表征，但其实验测定过程颇为繁琐，因为需要获取不同温度、不同表面活性剂浓度下SOW体系的相行为数据。本研究提出两种数学模型，用于快速预测油品的EACN。二者均采用人工智能（机器学习）方法构建，分别为神经网络（NN）与图机（GM）。其中GM模型依托包含111个已知EACN值分子的训练集的SMILES编码实现，而NN模型则以该111个分子经COSMOtherm软件计算得到的σ矩描述符作为输入。在前期研究环节中，针对现有数据集，研究采用留一法算法选取两种模型的适宜复杂度。对由10种复杂化妆品及香料分子组成的新测试集的液体EACN进行对比后发现，两种方法在准确性与可靠性方面表现相当。最后，将NN与GM模型应用于九组同系物化合物，结果显示GM模型得到的EACN变化趋势与实验结果的契合度优于NN模型的预测结果。基于σ矩描述符的NN模型以及GM模型所得的全部结果，可通过支持信息（Supporting Information）中详述的可下载演示工具进行复现。