Physics-Informed Neural Network Framework for Performance Prediction and Parameter Identification of Microbial Fuel Cells

Bioelectrochemical systems (BES) such as microbial fuel cells (MFCs) offer a promising route for sustainable wastewater treatment and bioelectricity generation. However, MFC modeling faces a structural dichotomy: mechanistic models provide physical interpretability but suffer from difficult calibration, while data-driven approaches offer predictive flexibility at the cost of mechanistic transparency and limited extrapolation. To reconcile these paradigms, we developed BioElec-PINN, a physics-informed neural network framework that couples sparse experimental data with a differential-algebraic bioelectrochemical model that distinguishes bulk and biofilm substrate compartments through a mass-transfer coefficient. This paper presents the BioElec-PINN architecture and evaluates its performance on fed-batch MFCs treating synthetic winery wastewater across varying organic loads. We trained the network to jointly reconstruct model-conditioned latent states and estimate ten regularized cycle-specific kinetic, transport, and electrochemical parameters. The BioElec-PINN achieved calibration voltage normalized root mean square error NRMSE values of 0.048–0.100. The inferred parameter sets were subsequently transferred without recalibration to a Radau IIA solver (classical solver), whose forward trajectories showed close cycle-level agreement and supported the cross-formulation dynamic consistency of the learned mechanistic parameterization. A matched Direct multilayer perceptron MLP was additionally evaluated using an interleaved held-out protocol in which approximately 40% of the observations were retained for training and the remaining 60% were used exclusively for raw-data evaluation. The Direct MLP achieved lower pointwise interpolation errors, with mean voltage and chemical oxygen demand (COD) NRMSE values of 0.064 and 0.146, compared with 0.121 and 0.206 for the BioElec-PINN, respectively. A conditional residual-bootstrap analysis based on 20 complete BioElec-PINN retrainings was used to quantify parameter uncertainty. Thirty-three of the forty cycle-specific estimates exhibited relative 95% interval widths below 1%, while the bootstrap correlation structure revealed coordinated kinetic, mediator, and electrochemical parameter groups. However, the unconstrained MLP introduced non-monotonic COD trajectories in three cycles and physically inadmissible continuation outside the observed interval, including negative voltage and substantial COD rebound. In contrast, the BioElec-PINN preserved monotonic substrate depletion and coupled voltage–substrate dynamics while reconstructing model-conditioned latent states and estimating regularized cycle-specific effective parameters. The framework therefore provides a physically structured inverse-calibration component for future MFC digital twins, with raw-data performance, physical admissibility, parameter transferability, and conditional uncertainty evaluated explicitly.