Enhancing purple non-sulfur bacteria modeling with physics-informed neural networks

In the pursuit of a resource-efficient economy, purple non-sulfur bacteria (PNSB) represent a promising solution due to their capacity to convert waste from various sources into valuable products, including biomass. However, scaling up PNSB technology remains challenging, and developing reliable dynamic models for monitoring and control is essential to facilitate this transition. Despite recent efforts dedicated to PNSB modeling, existing gaps in process understanding and difficulties in data collection still limit their development. In this regard, physics-informed neural networks (PINNs) emerge as a natural candidate, considering their ability to integrate partial physical information. This paper presents a PINN-based model developed by combining an existing first-principles model—whose performance declines under new conditions—with additional data representing these conditions. To assess the performance of the PINN-PNSB model, we compare it with other modeling alternatives, including the updated parametric model obtained by classical parameter identification and a pure artificial neural network (ANN). A PINN-derived model, obtained by updating the physical model parameters during PINN training, is also evaluated. Results using training and test data demonstrate the superior performance of the PINN-based model for PNSB applications.