EinFields Datasets

This repository contains examples of datasets used to train EinFields, a neural representation designed to compress computationally intensive four-dimensional numerical relativity simulations into compact implicit neural network weights. These datasets correspond to the work presented in the paper Einstein Fields: A Neural Perspective To Computational General Relativity.

EinFields models the metric, the core tensor field of general relativity, enabling derivation of physical quantities via automatic differentiation. Unlike conventional neural fields, EinFields are Neural Tensor Fields where dynamics emerge naturally. Key features include continuum modeling of 4D spacetime, mesh-agnosticity, storage efficiency, derivative accuracy, and ease of use.

Overview

The datasets include three examples used to train EinFields, namely Schwarzschild, Kerr, and Gravitational Wave (GW) metrics, provided in spherical, Kerr-Schild, and Cartesian coordinates.

Code

The associated code and framework for EinFields is available on GitHub: https://github.com/AndreiB137/EinFields

Usage

These datasets are designed to be used with the EinFields framework. For detailed installation instructions, examples on how to load and utilize these datasets for training, and further information on the framework's capabilities, please refer to the EinFields GitHub repository.

Citation

Paper: https://arxiv.org/abs/2507.11589

@article{
      title={EINSTEIN FIELDS: A NEURAL PERSPECTIVE TO COMPUTATIONAL GENERAL RELATIVITY},
      author={Cranganore, Bodnar and Berzins},
      year={2025},
      eprint={2507.11589},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}