A Hybrid PINN-DE Framework for Data-Driven Parameter Estimation of Tumor-Immune Dynamics in Bladder Cancer

Bladder cancer presents significant clinical challenges due to its complex immune microenvironment and highly heterogeneous response to treatments. To create accurate, individualized models of disease progression, we first construct a system of Ordinary Differential Equations (ODEs) that captures tumor-immune interactions. We address the challenge of estimating unknown parameters by performing a rigorous comparative analysis of two heuristic optimization methods: Differential Evolution (DE), a robust global optimization algorithm, and Physics-Informed Neural Networks (PINN), a novel machine learning framework that embeds ODE constraints into its loss function. Our findings provide a critical evaluation of the computational efficiency and accuracy of each method for parameterizing biological ODE systems. This study validates the power of hybrid machine learning approaches in mathematical oncology, yielding a data-driven model of bladder cancer progression with direct potential for optimizing personalized treatment strategies.