Investigating glucose-lactate metabolism in glioblastoma multiforme via universal physics-informed neural networks

Understanding the metabolic adaptations of cancer cells is crucial for uncovering potential therapeutic targets and improving treatment strategies. In this study, we present a hybrid modeling framework that combines Physics-Informed Neural Networks (PINNs) and Universal PINNs (UPINNs) to investigate glucose-lactate metabolism in glioblastoma cell lines. We first employed PINNs to infer critical model parameters governing glucose uptake and phenotypic switching in tumor cells, demonstrating high accuracy using synthetic data. We then extended this framework using UPINNs to uncover hidden metabolic dynamics that could not be explicitly modeled, introducing a latent variable $ W $ to represent unknown functional behavior in glycolytic processes. Our approach was validated for both synthetic and experimental datasets for two glioblastoma cell lines (LN18 and LN229) with distinct metabolic phenotypes. The UPINN framework not only captured cell-type-specific behaviors but also remained robust in the presence of moderate experimental noise. Furthermore, we explored the sensitivity of the model to the trade-off between data fidelity and mechanistic constraints, showing that the choice of loss term weighting significantly impacts predictive performance. While our application centered on cancer metabolism, the proposed method was general and applicable to a wide range of systems described by differential equations, including problems in biology, engineering, and physical sciences. This work demonstrates the potential of UPINNs as a powerful and interpretable tool for data-driven discovery in partially observed dynamical systems.