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. Author summaryBladder 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 patients disease will progress, researchers use mathematical models that simulate the "war" between cancer cells and the immune system. However, these models are only useful if they can be accurately tuned to a specific patients 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 "survival of the fittest" 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 patients 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.