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

arXiv: https://arxiv.org/abs/2302.07405 · HTML: https://mlsanity.com/paper/2302.07405/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 66 references that are in the map.
- First posted on arXiv 15 Feb 2023.

## Builds on (most cited first, 8 of 8)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Skillful Precipitation Nowcasting using Deep Generative Models of Radar](https://mlsanity.com/paper/2104.00954/) (2021)
- [Why Deep Neural Networks for Function Approximation?](https://mlsanity.com/paper/1610.04161/) (2016)

## Abstract (arXiv)

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.