Unsupervised physics-informed neural network in reaction-diffusion biology models (Ulcerative colitis and Crohn's disease cases) A preliminary study

Résumé : We propose to explore the potential of physics-informed neural networks (PINNs) in solving a class of partial differential equations (PDEs) used to model the propagation of chronic inflammatory bowel diseases, such as Crohn's disease and ulcerative colitis. An unsupervised approach was privileged during the deep neural network training. Given the complexity of the underlying biological system, characterized by intricate feedback loops and limited availability of high-quality data, the aim of this study is to explore the potential of PINNs in solving PDEs. In addition to providing this exploratory assessment, we also aim to emphasize the principles of reproducibility and transparency in our approach, with a specific focus on ensuring the robustness and generalizability through the use of artificial intelligence. We will quantify the relevance of the PINN method with several linear and non-linear PDEs in relation to biology. However, it is important to note that the final solution is dependent on the initial conditions, chosen boundary conditions, and neural network architectures.