# Adapting Physics-Informed Neural Networks for Bifurcation Detection in Ecological Migration Models

arXiv: https://arxiv.org/abs/2409.00651 · HTML: https://mlsanity.com/paper/2409.00651/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 14 references that are in the map.
- First posted on arXiv 1 Sep 2024.

## Builds on (most cited first, 6 of 6)

- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Physics-informed neural networks for inverse problems in supersonic flows](https://mlsanity.com/paper/2202.11821/) (2022)
- [The Old and the New: Can Physics-Informed Deep-Learning Replace Traditional Linear Solvers?](https://mlsanity.com/paper/2103.09655/) (2021)
- [Investigating molecular transport in the human brain from MRI with physics-informed neural networks](https://mlsanity.com/paper/2205.02592/) (2022)
- [Physics-informed Neural Networks-based Model Predictive Control for Multi-link Manipulators](https://mlsanity.com/paper/2109.10793/) (2021)
- [Interval and fuzzy physics-informed neural networks for uncertain fields](https://mlsanity.com/paper/2106.13727/) (2021)

## Abstract (arXiv)

In this study, we explore the application of Physics-Informed Neural Networks (PINNs) to the analysis of bifurcation phenomena in ecological migration models. By integrating the fundamental principles of diffusion-advection-reaction equations with deep learning techniques, we address the complexities of species migration dynamics, particularly focusing on the detection and analysis of Hopf bifurcations. Traditional numerical methods for solving partial differential equations (PDEs) often involve intricate calculations and extensive computational resources, which can be restrictive in high-dimensional problems. In contrast, PINNs offer a more flexible and efficient alternative, bypassing the need for grid discretization and allowing for mesh-free solutions. Our approach leverages the DeepXDE framework, which enhances the computational efficiency and applicability of PINNs in solving high-dimensional PDEs. We validate our results against conventional methods and demonstrate that PINNs not only provide accurate bifurcation predictions but also offer deeper insights into the underlying dynamics of diffusion processes. Despite these advantages, the study also identifies challenges such as the high computational costs and the sensitivity of PINN performance to network architecture and hyperparameter settings. Future work will focus on optimizing these algorithms and expanding their application to other complex systems involving bifurcations. The findings from this research have significant implications for the modeling and analysis of ecological systems, providing a powerful tool for predicting and understanding complex dynamical behaviors.