cstrohmy/molecular-schr-dinger-via-pinns

An approach to the (time-independent) molecular Schrödinger equation via physics-informed neural networks (PINNs).

Molecular Schrödinger via PINNs

Table of Contents

• Introduction
• Objective
• Installation
• Usage
• Results
• License

Introduction

This project aims to solve the time-independent molecular Schrödinger equation by employing physics-informed machine learning techniques. A cornerstone of molecular physics, understanding electron distributions within molecules is essential for ascertaining their chemical properties.

Objective

The main objective is to find eigenvalues and eigenstates of the time-independent Schrödinger operator for the Hydrogen atom. Currently, the project generates exact solutions for the Hydrogen atom as a baseline and attempts to approximate these solutions using Physics-Informed Neural Networks (PINNs).

Installation

1. Clone the repository to your local machine: ```bash git clone https://github.com/your_username/molecular-schrodinger-solver.git ```
2. Navigate to the project directory: ```bash cd molecular-schrodinger-solver ```
3. Install dependencies (assuming you have Python and pip installed): ```bash pip install tensorflow numpy scipy ```

Usage

To generate exact solutions for the Hydrogen atom, run:

```bash python hydrogen.py ```

To solve the Schrödinger equation for the Hydrogen atom using PINNs, run:

```bash python hydrogen-pinn.py ```

Results

The project currently provides exact solutions for the Hydrogen atom, serving as a benchmark. Comparison of these exact solutions with those obtained from the PINN model will be conducted as the project evolves.

License

This project is licensed under the MIT License - see LICENSE.md for details.