Mechanistic Hybrid model for Algal growth

This data set constitutes a dynamic model and hybrid modeling approach for microalgae growing on nitrate and degrading azithromycin in batch studies. Relevant codes for estimation of the apparent yield coefficient for nitrate/biomass and azithromycin/biomass production, and an initial guess for the dynamic model parameter using a custom-function curve-fitting approach. Derivative approximations from interpolated concentration vectors, after ignoring the nonphysical estimates (e.g., negative growth rates, positive rate for nitrate concentration), were concatenated. Two different mechanistic models adopted the normalized sum of squared errors (between measured and simulated profiles), combined with an L2 regularization term, served as the objective function to be iteratively minimized. The hybrid modeling strategy maintains system ODEs as a mechanistic modeling framework while replacing poorly characterized, time-varying terms with flexible, data-driven sub-models. In the present study, one-HL with a limit of 10 neurons or two-HLs with 5 neurons in each layer, tansig, and purelin activations were considered. To assess model sensitivity, small Gaussian noise perturbations (±10%) were applied to each parameter, and the model was simulated 500 times, each time with a set of perturbed parameters. The confidence interval of simulated states at each time point maps to the prediction interval (95%) band for each state variable.