Input Consistency Regularization of Experimental Data for Modeling Functional Characteristics of A2M3O12 Family of Compounds

The prediction confidence is one of the goals of any machine learning-based study with no respect if this is distinguished as the aim of the study or is the associated desired concomitant. The possibility do not import the additional error into the pre-experimental estimation of the studied characteristics should be the goal of machine learning-based approaches in any case limited in their accuracy by the precision and confidence of the experimental data. The representation theory and information geometry come to the fore to achieve the stated desiderates. In this study, the approaches related to the input consistency regularization are considered which may provide with the required enhancement in the prediction confidence and are able to recoup the part of the experimental error associated with obtaining the data using the methods of different precision or with the discrepancy in the results obtained. The methodology of regularization of the input data consistency is considered in this study in relation to the problem of the predictive modeling of the functional characteristics of ${\mathrm{A}}_2{\mathrm{M}}_3{\mathrm{O}}_{12}$ family of ceramics with negative/close-to-zero thermal expansion (NTE or ZTE) properties. It is showed that using diffusion models as the input consistency regularization procedure allows one to achieve the reduction in predictive error for about thirty percent in its absolute value. The Hessian-based analysis of the loss function landscape is considered as the criterion of the generalizability and model performance. The continuity of the property change as a function of the data description coupled with the analysis of p-values for the experiment-prediction output are considered as the auxiliary criteria concerned with the input consistency regularization.