Controlled Adaptation of a Hybrid Neural–Mechanistic Framework to Correct Parameter-Distorted SIR Dynamics Through Coupling Optimization

This study investigates, in a controlled setting, a hybrid neural–mechanistic correction framework applied to a parameter-distorted or biased epidemiological SIR model. The aim was to explore to what extent a residual neural component can compensate for mechanistic model error, how strongly reconstruction quality depends on Savitzky–Golay-based derivative estimation, how robust the framework remains under increasing observational noise, and how the coupling parameter λ should be selected. The distorted mechanistic SIR model was coupled with a feedforward neural network trained on residual dynamics estimated from noisy synthetic observations. Savitzky–Golay smoothing was evaluated on a parameter grid, while λ was determined by continuous numerical optimization over the interval 0, 1. The experiments were repeated using multiple random seeds and examined at three different noise levels. The hybrid model consistently improved reconstruction compared to the distorted mechanistic baseline across the entire investigated noise range. The results indicate that performance depended on the preprocessing applied for derivative estimation. The optimized coupling parameter remained in the high range in all cases, suggesting that substantial neural correction is advantageous in the presence of parameter bias. The results show that residual neural correction can be successfully transferred to an epidemiological SIR setting.