A Transformation Matrix Explains the Sequential Forecasting Data-Driven Deep Learning Model

Deep learning (DL) data-driven models (DDMs) offer significant potential for predicting nonlinear events, particularly in the absence of an analytical or known mathematical foundation. This study provides the first empirical evidence of a transformation matrix derived from a data-driven DL model for the sequential prediction of physical properties, where both the input and output are single-variable time series. The matrix's performance is tested on two different datasets to evaluate its effectiveness, demonstrating substantial proficiency in prediction modeling. The mathematical approach is explained, and the results are presented. Different portions of the training sets (60% and 80%) are examined, showing significant prediction accuracy. Furthermore, the DDM DL transformation matrix is square, has eigenvalues, and is able to reveal the correlations, stability, and limits of the system in which the model is used. This approach has the potential to provide explainable insights into data-driven DL models.