This repository showcases a basic implementation of Neural Ordinary Differential Equations (ODEs), a groundbreaking concept by Chen et. al that introduces a novel family of neural networks.

Welcome to the Neural Ordinary Differential Equations (Neural ODEs) repository! Here, we delve into the fascinating realm of Neural ODEs, a revolutionary concept introduced by Chen et al. that reimagines neural networks through the lens of ordinary differential equations. This repository serves as a small guide to understanding, implementing, and experimenting with Neural ODEs.

Neural ODEs are a groundbreaking approach that challenges the traditional architecture of neural networks. Instead of the conventional stacked layers of neurons, Neural ODEs harness the power of differential equations to model hidden layers. This not only leads to elegant and flexible architectures but also provides a deeper mathematical understanding of neural networks' dynamics. The core idea behind Neural ODEs is the use of continuous-depth models. In a standard neural network, data is processed layer by layer, with each layer applying a specific transformation. Neural ODEs, on the other hand, treat the transformation between layers as a continuous process governed by ordinary differential equations. This means that the network's hidden states evolve continuously, allowing for a more natural representation of dynamic systems.

To dive into the technical details and the original research paper, check out the concept's pioneering work.

• Innovative Architecture: Explore an unconventional neural network design that leverages ordinary differential equations to define hidden layers.
• Flexibility and Expressiveness: Neural ODEs offer a seamless way to model continuous transformations, enabling more expressive and adaptive networks.
• Continuous Depth: Unlike traditional architectures with fixed depths, Neural ODEs allow continuous depth, offering an intriguing perspective on network scalability.
• Interpretable Dynamics: Gain insights into the inner dynamics of neural networks by visualizing the evolution of states over time.

Neural ODEs find applications in various domains due to their unique properties. Some notable use cases include:

• Time Series Analysis: Neural ODEs are adept at capturing temporal dependencies in time series data, making them suitable for tasks like forecasting and anomaly detection.

• Optimization and Physics Simulation: Neural ODEs can simulate physical systems and optimize parameters by learning the underlying dynamics.

The parametric law describing the behavior of a hypothetical dynamical system, solved by Neural ODEs, is described as follows:

$$ \displaylines{x' = a_1x + b_1y + c_1e^{-d_1t} \\ y'= a_2x + b_2y + c_2e^{-d_2t} \\ x(0)=0 \\ y(0)=0} $$

.
│   .gitignore
│   README.md
│   requirements.txt
│
├───figures
│       Figure_1.png
│
└───src
        main.py

1. Clone the Repository: Begin by cloning this repository to your local machine using the following command:

   git clone https://github.com/hassanmoin980/eco-systems-neural-odes.git
   

2. Install Dependencies: Navigate to the repository folder and install the required dependencies:

   cd eco-systems-neural-odes
   pip install -r requirements.txt
   

3. Explore Examples: Dive into the src/ directory to find the script showcasing a simple application of Neural ODEs.

Contributions are welcomed from the community to enhance and expand the Neural ODE repository. Whether it's fixing bugs, adding new features, or improving documentation, your efforts are greatly appreciated. To contribute, follow these steps:

1. Fork the repository.
2. Create a new branch for your feature or bug fix.
3. Make your changes and commit them with descriptive messages.
4. Push your changes to your fork.
5. Submit a pull request, detailing the changes you've made and their significance.