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

**Authors:** Ahmed Rebai, Louay Boukhris, Radhi Toujani, Ahmed Gueddiche, Fayad Ali Banna, Fares Souissi, Ahmed Lasram, Elyes Ben Rayana, Hatem Zaag  
**arXiv:** [2302.07405](https://arxiv.org/abs/2302.07405)  
**Date:** 2023-02-15  
**Summary page:** https://www.summarizepaper.com/en/paper/2302.07405v1/

## Key points

- Study aims to explore Physics-Informed Neural Networks (PINNs) for solving Partial Differential Equations (PDEs) in Chronic Inflammatory Bowel Diseases (IBDs)
- Prioritization of unsupervised deep neural network training due to complex biological systems and limited data availability
- Emphasis on reproducibility, transparency, robustness, and generalizability through Artificial Intelligence
- Importance of precise collection and examination of endoscopic video data for disease identification and classification
- Discussion on Physics-Informed Machine Learning (PIML) merging physics concepts with advanced machine learning techniques
- Overview of the establishment of neural networks in mathematics, including DeepFNet architecture for functional approximation tasks
- Exploration of scenarios where traditional machine learning techniques may be more suitable based on system dynamics
- Anticipation of widespread adoption of PINN and PIML technologies in biology and medicine for real-world problem-solving

## Summary

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In this study, we aim to explore the potential of Physics-Informed Neural Networks (PINNs) in solving Partial Differential Equations (PDEs) that model Chronic Inflammatory Bowel Diseases (IBDs), such as Crohn's disease and ulcerative colitis. The use of unsupervised deep neural network training is prioritized due to the complexity of the underlying biological system, characterized by intricate feedback loops and limited high-quality data availability. Our goal is to assess the effectiveness of PINNs in solving PDEs while emphasizing reproducibility and transparency in our approach, with a focus on ensuring robustness and generalizability through Artificial Intelligence. Furthermore, we will delve into the importance of precise collection and examination of endoscopic video data for identifying disease presence and advancement, as well as categorizing different types of IBDs and classifying subtypes within the same disease. Additionally, we will discuss Physics-Informed Machine Learning (PIML), which merges physics concepts with advanced machine learning techniques like neural networks to enhance model precision in systems governed by PDEs. This emerging discipline has shown success in various fields such as fluid dynamics, structural mechanics, quantum mechanics, cosmology, and quantitative finance. The establishment of neural networks in mathematics dates back to Cybenko's work in 1989 on universal approximation capabilities. Various architectures have since been developed, including DeepFNet, which excels at functional approximation tasks by modeling complex relationships with fewer neurons than shallow networks. We will also explore scenarios where traditional machine learning techniques are more suitable due to either a lack or abundance of physical models describing system dynamics. With continued growth and development in PINN and PIML technologies expected to reach their peak potential before settling into a plateau of productivity, we anticipate their widespread adoption for solving real-world problems in biology and medicine. Through this comprehensive exploration and analysis, we aim to contribute valuable insights towards advancing the understanding and treatment of chronic inflammatory bowel diseases using cutting-edge AI-driven approaches.