[Analysis Example] Estimating Physical Properties Using σ-profile as Descriptors in Machine Learning

The σ-profile is represented by a spectrum and is used to predict various physical properties. Normally, a quantum chemical calculation is required to obtain the σ-profile, but J-OCTA uses a machine learning model, the Graph Convolutional Network （GCN）, to rapidly estimate ^[3] it from SMILES, a molecular notation.

In this study, we compared the σ-profiles obtained from quantum chemical calculations and GCN. Gaussian was used for the quantum chemical calculation.

Figure 1 shows the results of the estimation. It can be seen that the results are in good agreement with the results of quantum chemical calculations.

We present an example of using the σ-profile, a descriptor of the COSMO method, as a feature for machine learning to predict physical properties. The J-OCTA machine learning function （MI-Suite） was used to build the model and prepare features to predict the glass transition temperature （Tg）. The data set for Tg was taken from ^[4]. The data obtained includes the SMILES and Tg values for each compound.

The procedure for learning and predicting Tg is as follows:

1. 1. The descriptor calculation function was used to deduce the σ-profile from the SMILES of each compound.
2. 2. Learning was performed with the deduced σ-profile as the input value and Tg as the target value.
   The settings for learning are as follows:
   • - Among the learning methods supported by MI-Suite's learning function, XGBoost, a boosting-based learning method, was used.
   • - The data ratio of the training and test sets was 8:2.
3. 3. The estimated σ-profiles were mapped using UMAP ^[5] and color-coded by Tg value.
   • - UMAP is a dimensionality reduction method that visualizes multidimensional space and improves interpretability.
   • - In this case, a 51-dimensional σ-profile was mapped to a two-dimensional space.

Figure 2 shows the training results. The prediction accuracy was 𝑅²=0.999 for the training data and 𝑅²=0.942  for the test data, based on the coefficient of determination. Mapping results are shown in Figure 3. It can be observed that the feature indicated by the x-axis affects Tg, while the y-axis indicates another feature that has little to do with Tg. The plot of σ-profiles for points where only the x value differs significantly shows that the feature concentrated in x is the polarity of molecules.