Application of Physics-Informed Neural Networks (PINNS) to Solve a Dynamic Model of Drug Abuse

Abstract

Drug abuse remains a complex and persistent issue in Indonesia, requiring a systematic approach to understand its underlying dynamics. This study applies Physics-Informed Neural Networks (PINNs) as an alternative method for solving the nonlinear differential equations of the SnSeIR drug abuse dynamics model. The model divides the population into four compartments: susceptible individuals without education (Sn), susceptible individuals with education (Se), active users (I), and individuals who have quit or completed rehabilitation (R). The focus of this research is the forward problem, in which the solution of the model is approximated using parameter values obtained from the literature. The PINNs framework combines a data loss term, which measures the discrepancy between predicted solutions and synthetic data, and a physics loss term that enforces consistency with the governing differential equations. The performance of PINNs was first validated by comparing its results with synthetic data generated using the classical fourth-order Runge–Kutta (RK4) method. The model was then further tested using additional synthetic datasets to evaluate generalization. The findings demonstrate that PINNs can successfully approximate the solution of the SnSeIR model, yielding continuous and mathematically consistent trajectories that align with the system’s dynamics. Moreover, the mesh-free nature of PINNs provides flexibility and computational efficiency, highlighting its potential as a promising tool for analysing complex population-based models.