PDE-Simulation-and-Compression

A numerical simulation project to solve the 1D heat equation and apply dimensionality reduction techniques using PCA for data compression. This repository is a comprehensive demonstration of solving Partial Differential Equations (PDEs) numerically and validating the effectiveness of data compression techniques.

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Features

1. Numerical Simulation:

   • Solves the 1D heat equation using the finite difference method (FDM).
   • Simulates temperature distribution over time in a rod with defined initial and boundary conditions.

2. Dimensionality Reduction:

   • Applies Principal Component Analysis (PCA) to compress simulation data.
   • Validates compression quality with reconstruction error metrics like Mean Squared Error (MSE).

3. Visualization:

   • Plots:
     • Temperature evolution over time.
     • Original vs. Reconstructed data.
     • Compression error over time.

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Getting Started

Prerequisites

• Python 3.x
• Required Libraries:
  • numpy
  • matplotlib
  • scikit-learn

Installation

1. Clone the repository:

   git clone https://github.com/shrusti-stars/PDE-Simulation-and-Compression.git
   cd PDE-Simulation-and-Compression