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Numerical Methods and AI Algorithms

This project contains implementations of various numerical methods and artificial intelligence algorithms, including animations to visualize their working.

About the Project

Features

  • Finite Element Method (FEM): Simulates rectangle'sdeformation in a 2D mesh.
  • Monte Carlo Method: Estimates the value of π using a random sampling technique.
  • Runge Kutta: Solves the pendulum motion and visualizes energy changes over time.
  • Genetic Algorithm: Finding minimize value of a function=x**2+4*sin(5x)+cos(10x) using evolutionary techniques.
  • PINN (Physics-Informed Neural Network): Solves differential equations for pendulum motion.
  • Gradient Descent: Finds the minimum of a quadratic function=x**2+4x+4.

Usage

Each algorithm is modularized and can be run independently. Examples for each algorithm are in the examples/ directory.

Installation

pip install -r requirements.txt

Examples

Run any example script to see the algorithm in action. For example:

python examples/fem_example.py

License

MIT License