Hybrid modeling of photocatalytic contaminant degradation using nanomaterials synthesized with microalgal extracts

Synthetic dyes released through industrial effluents pose significant environmental risks due to their persistence and toxicity. Photocatalytic degradation through metal nanoparticles offers a promising, eco-friendly remediation approach. This study presents a hybrid modeling framework for simulating the visible-light-driven degradation of Brilliant Blue R using silver nanoparticles (AgNPs) synthesized through extracts of Haematococcus pluvialis, Spirulina platensis, and Chlorella vulgaris. The biogenic AgNPs exhibited favorable physicochemical properties, including crystalline sizes of 13–16 nm and band gap energies between 2.17 and 2.33 eV. A simplified deterministic model was first developed, accounting for adsorption–desorption equilibrium and degradation kinetics, which enables analytical estimation of key kinetic parameters. These parameters were used to train artificial neural networks (ANNs) that map experimental conditions such as light intensity, dye concentration, nanoparticle dosage, and pH to degradation kinetics. To overcome the limited size of datasets obtained through experiments, a novel data augmentation strategy was implemented using Gaussian noise derived from measurement uncertainty and confidence intervals of the deterministic model's parameters. This strategy enabled the significant augmentation of data enhancing the ANN performance. Indeed, the global mean squared error dropped from 5.6 × 10−4 to 1.3 × 10−5 for AgNPs from H. pluvialis, from 1.6 × 10−2 to 3.3 × 10−6 for C. vulgaris, and from 2.4 × 10−3 to 4.2 × 10−4 for S. platensis when using both input and output augmentation. The proposed hybrid framework couples mechanistic interpretability with data-driven prediction providing a reliable tool for optimizing photocatalytic degradation processes via sustainable nanomaterials of microalgal origin.