A Physics‐Informed Neural Network Framework for Tumor‐Immune Interactions, Metastatic Invasion, and Haptotaxis Systems

ABSTRACT Cancer and tumor growth are complex biological processes that can be modeled using systems of ordinary differential equations (ODEs) and partial differential equations (PDEs). These models capture the dynamics of tumor progression, interactions with the immune system, and responses to treatments. However, solving these equations accurately and efficiently remains a challenge, particularly when dealing with patient‐specific data and complex spatial distributions. This paper proposes the use of physics‐informed neural networks (PINNs) as a novel approach to solve ODE and PDE models of cancer and tumor growth. PINNs embed physical laws directly within the architecture of the neural network, enabling accurate predictions while leveraging the flexibility of deep learning techniques. We demonstrate the effectiveness of PINNs in modeling various aspects of tumor dynamics, including growth patterns, immune interactions, and treatment responses. Furthermore, we derive bounds on the generalization error, linking training residuals to quadrature errors and validating PINNs' reliability for coupled biological systems.