thomashelfer / torchgrtl

A translation of crucial parts of GRTL in torch for accelerated learning

TorchGRTL - Numerical General Relativity in PyTorch

Overview

TorchGRTL is a Python library that provides a PyTorch-based implementation of key components of GRTL codebase . It uses GPU optimisation and Autodiff of PyTorch to accelerate computations to improve black hole simulations.

Installation

Prerequisites

Before installing TorchGRTL, ensure you have the following prerequisites:

• Python 3.8 or higher
• pip package manager

Steps

1. Clone the TorchGRTL repository:

   git clone https://github.com/ThomasHelfer/TorchGRTL.git
   cd TorchGRTL

2. Install the package:

   pip install .

3. (Optional) Set up pre-commit hooks for code formatting and linting:

   pre-commit install

Usage

The TorchGRTL library offers powerful tools to compute a variety of quantities essential in numerical relativity. Here are some examples of how you can use the library:

Computing Christoffel Symbols

You can compute the Christoffel symbols, which are crucial in the context of general relativity for defining the Levi-Civita connection and geodesic equations:

# Compute the Christoffel symbols using the standard method
chris = compute_christoffel(d1['h'], h_UU)

In these examples, d1['h'] refers to the first derivatives of the metric tensor, and h_UU is the inverse metric tensor.

Calculating Hamiltonian and Momentum Constraints The library can also compute more complex quantities like the Hamiltonian and Momentum constraints, which are fundamental in ensuring the consistency of solutions in numerical relativity:

# Compute the Hamiltonian and Momentum constraints
out = constraint_equations(vars, d1, d2, h_UU, chris)

Here, vars contains various tensor fields, d1 and d2 are the first and second derivatives of these tensor fields, and chris is the computed Christoffel symbols.

Self-Contained Example

For a full, self-contained example that demonstrates the library's capabilities, refer to example.py in the repository. This example will guide you through a typical use case, showing how to leverage TorchGRTL for numerical relativity simulations and calculations.

License

TorchGRTL is released under the MIT License. See LICENSE for more details.

Contact

For questions or support, please contact Thomas Helfer at [email protected].