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

Abstract 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 robust computational framework for parameter estimation and providing a necessary algorithmic foundation for future personalized treatment strategies. Author summary Bladder cancer remains a major global health threat, characterized by highly unpredictable responses to treatment and a high likelihood of recurrence. To better predict how a patient’s disease will progress, researchers use mathematical models that simulate the interactions between cancer cells and the immune system. However, these models are only useful if they can be accurately tuned to a specific patient’s data—a process called parameter estimation. This task is notoriously difficult because clinical data is often sparse and noisy, making it hard to find the right settings for the model. In this study, we developed a novel computational framework that combines a traditional optimization algorithm (Differential Evolution) with Physics-Informed Neural Networks (PINNs), a specialized architecture designed to embed physical constraints directly into the learning process. By “teaching” the AI the underlying biological laws of cancer growth, our hybrid approach can accurately estimate a patient’s unique disease parameters even when raw data is limited. We validated this method using a “virtual patient” system derived from real-world clinical trials. Our results show that this hybrid approach provides a more robust and reliable way to personalize cancer models, offering a powerful new tool for doctors to simulate and optimize individual treatment plans before they are even administered. Competing Interest Statement The authors have declared no competing interest. Footnotes A section titled Assumptions and Clinical Data Limitations has been added; Figures have been updated; Minor changes to notation for clarification.