  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.
