PHYSICS-INFORMED NEURAL NETWORKS FOR SPATIOTEMPORAL TUMOR GROWTH MODELING: A COMPREHENSIVE SIMULATION STUDY

Abstract

Mathematical modeling of tumor growth using partial differential equations (PDEs) has emerged as a powerful tool for understanding cancer progression and optimizing therapeutic strategies. However, traditional numerical methods face significant challenges when applied to complex geometries, sparse clinical data, and inverse parameter estimation problems. This study employs Physics-Informed Neural Networks (PINNs) — a deep learning framework that embeds PDE constraints directly into the neural network training — to solve the Fisher--Kolmogorov--Petrovsky--Piskunov (Fisher--KPP) reaction-diffusion equation in a two-dimensional spatial domain. The PINN framework successfully captures the spatiotemporal evolution of tumor cell density from an initial Gaussian seed through progressive invasion and saturation. We present comprehensive 2D contour visualizations and 3D surface reconstructions at six time points (t=0.0,1.0,2.0,3.0,4.0,5.0), demonstrating the characteristic traveling wave behavior of the Fisher--KPP model. The results confirm that PINNs provide a mesh-free, data-efficient, and robust computational framework for tumor growth modeling, with strong potential for patient-specific parameter inference and treatment planning. Furthermore, we discuss the implications of our findings for personalized radiotherapy and the integration of PINNs with multimodal clinical imaging data.