README.md

In this repository you can find codes for solving edps and edos by neural networks.

First, the problems have been approximated through an interpolation or adjustment. As in the case of a simple edo and systems such as the Prey-Predator model and SIR.

Finally, ODE's and PDE's have been solved through PINNs (Physics-Informed Neural Networks). As is the case of a simple ODE, SIR model, Prey-Predator model and the heat equation.

🌊 Solving ODEs & PDEs with Neural Networks 🤖

📖 Description

Welcome to this repository! Here, you will find codes for solving Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs) using neural networks.

🚀 What’s Included

1. 📊 Approximation Methods: The problems are first approximated through interpolation or fitting. Examples include:
   • A simple ODE
   • Systems like the Prey-Predator model 🐾
   • The SIR model for disease spread 🦠
2. 🧠 Physics-Informed Neural Networks (PINNs): We leverage PINNs to solve both ODEs and PDEs. Implementations include:
   • A simple ODE
   • SIR model
   • Prey-Predator model
   • The heat equation 🔥

🔍 What You’ll Find Here

• 📚 Model Implementations: Neural network models designed for ODE and PDE solutions.
• 💡 Practical Examples: Real-world applications demonstrating the effectiveness of neural networks in solving differential equations.
• 📝 Documentation: Step-by-step instructions for setting up the environment, running models, and interpreting results.
• 🔗 Resources: Relevant articles, tutorials, and research papers for further reading.