Dynamic modeling of PISA achievement scores: comparative analysis of artificial neural networks and differential equation systems approaches

In this study, the effects of nine key educational problems in schools on student achievement in mathematics, science, and reading in the Programme for International Student Assessment (PISA) were examined using artificial neural networks and differential equation systems. A linear differential equation model was used to describe instantaneous changes over time for twelve variables. Furthermore, the structure in which the nine education-related variables were defined as inputs and the PISA scores as outputs was analyzed through a neural network model with a tangent hyperbolic activation function. Model parameters were estimated using a least-squares curve fitting procedure, and numerical simulations were implemented to evaluate model accuracy. The performance of the models was evaluated using statistical metrics such as root mean square error, sum of squared errors, and the coefficient of determination. Both approaches yielded high accuracy, which is expected given the low variability and aggregated nature of the national-level indicators; however, the neural network model produced slightly lower error levels and a stronger overall fit. Fractional-order differential equation simulations were also explored; however, they did not provide performance improvements relative to the ODE and ANN approaches. In addition, the effects of factors related to problems in education on each PISA score were determined using a neural network-based sensitivity analysis, and the most influential variables were reported. Finally, short-term scenario-based extrapolations of PISA scores for Türkiye were generated using the differential equation model, purely as mathematical extensions of the fitted trends.