Dynamic Modeling of PISA Achievement Scores: Comparative Analysis of Artificial Neural Networks and Differential Equation Systems Approaches

Abstract In this study, the effects of 9 different educational problems in schools on 3 different PISA scores were examined using Ordinary Differential Equation (ODE) and Artificial Neural Network (ANN) models. A linear ODE system was used to model instantaneous changes over time for a total of 12 variables. Furthermore, the structure, in which nine education-related variables were defined as inputs and PISA scores were defined as outputs, was analyzed through an ANN model with a Tangent Hyperbolic (tanh) activation function. The analyses were carried out using data for Türkiye. The fixed parameters of the ODE model were solved with the RungeKutta45 method using Matlab 2025a and estimated according to the minimum error criterion with the lsqcurvefit function. The ANN model was structured with activation functions, weights, and bias values. The performance of the models was evaluated using statistical metrics such as Root Mean Square Error (RMSE), Sum Square Error (SSE), and \(\:R²\). The results revealed that both methods predicted PISA scores very successfully, but the ANN model performed superiorly, with slightly lower error rates and correlation coefficients overall. Moreover, the ODE model was expressed with fractional-order differential equations (FODEs) and numerical simulations were carried out for 6 different derivative orders, but the FODE model performed behind the other two models. In addition, the effects of factors related to problems in education on each PISA score were determined quantitatively using ANN-based impact analysis, and variables with significant effects were reported in detail. Finally, 3-year PISA score estimates for Türkiye are presented with the ODE model. This study provides valuable insights for policy makers and educational scientists by modeling the complex dynamics of multiple factors in education on PISA achievement with both mathematical and artificial intelligence approaches.