Mechanistic Hybrid model for Algal growth
Description
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.
Files
Steps to reproduce
The modeling exercise codes are presented in three folders. One folder contains common codes, and the other two contain mechanistic and hybrid modeling workflows. For the mechanistic model, a1_interpolation_Rates calculates interpolated rates, and a2_Guess_values uses those estimates to have "guess values" of model parameters to be used in the dynamic model. "b1_mechanism1_Algae" is used for mechanistic model development (for both variants), while "b1a_mechanism1_bootgenerator" generates bootstrapped confidence intervals. "b2_histogram_boot" generates a distribution of those parameters. The "b3_prediction_interval_correct" generates a prediction interval of dynamic model profiles. b4_mechanism1_tim_varying—overlapping time domain (data points) for parameter estimation. For hybrid modeling, "M4_any_HL_Full_hybrid.m" does the hybrid modeling exercise. "M5_cross_val" is for cross-validation. M6_Hybrid_prediction uses random perturbation of hybrid model parameters for prediction interval estimation. M7_LIME_Shaply_creator generates Shapley values for the data-driven components.
Institutions
- Karunya UniversityTamil Nadu, Coimbatore