A hybrid metabolic graph neural networks based observer for metabolic modeling with sparse data

In this work a dynamic modeling framework for metabolic systems that combines metabolic graph neural networks (MGNNs) with nonlinear state estimation is developed to address the problems of sparseness and noisiness in bioprocess data. The MGNN architecture embeds known metabolic reaction connectivity into the model structure, restricting information flow to biochemically plausible interactions and reducing the number of trainable parameters relative to fully connected neural networks. To enable the estimation of unmeasured metabolites, the MGNN is coupled with an extended Kalman filter (EKF), which performs recursive state estimation using partial and noisy measurements. The framework is evaluated using two systems with distinct metabolic characteristics: Escherichia coli undergoing diauxic growth and a reduced oxidative stress network for Bordetella pertussis. Across both case studies, the MGNN-EKF observer yields lower estimation error and improved robustness to noise compared with a fully connected neural network under matched training conditions, for spare data scenario. Empirical observability analysis based on Gramian metrics validates the theoretical reconstructability of these states. These results indicate that embedding metabolic structure into data-driven dynamic models and coupling it with a state estimator improves predictions in bioprocess systems with limited measurements.