A reduced-order hybrid model for photobioreactor performance and biomass prediction

This paper introduces a hybrid approach for photobioreactor modeling tailored to microalgae cultivation, combining data-driven and mechanistic concepts to improve modeling efficiency and practicality for industrial scale-up applications. Most growth models for microalgae are nonlinear and require experimental measurement of several parameters. The aim of this work is to develop linear practical models for monitoring purposes. A model based on linear coefficients and polynomial features is proposed, balancing interpretability with nonlinear representation focusing on model transparency. To simplify the growth model, Taylor series expansion is applied to the Monod and logistic population models. Two scale-specific models are developed and evaluated, offering practical solutions for monitoring microalgae growth in photobioreactors. Therefore, this reduced order representation allows the biomass growth rate to be dependent directly on the biomass concentration. These models do not require exhaustive data collection of substrate concentration over time, making them costeffective and efficient for industrial applications. This work provides a step forward in photobioreactor modeling, contributing to the sustainable production of microalgae.