First Experiences on Exploiting Physics-Informed Neural Networks for Approximating Solutions of a Biological Model

Recent advances in artificial intelligence have changed the ability to study and model complex biological phenomena. Physics-Informed Neural Networks (PINNs) represent a novel approach that link deep learning techniques with fundamental physical principles in solving partial differential equations. This work proposes an implementation of PINNs for modeling tumor-induced angiogenesis through a system of coupled reaction-diffusion equations that track the interplay between different biological agents. We introduce a computational framework that combines neural network architectures with physics-based constraints, using an optimized loss function incorporating both empirical data and theoretical principles via strategic collocation points. Experimental results validate the reliability of our approach in predicting the intricate spatial and temporal patterns of blood vessel formation, showing the potential of PINNs as a robust computational tool for simulating complex biological processes.