Einstein Fields: A Neural Perspective To Computational General Relativity
This work addresses the problem of scalable and efficient computational general relativity for researchers in physics and numerical simulations, though it appears incremental as it adapts neural fields to a specific domain.
The authors tackled the computational intensity of four-dimensional numerical relativity simulations by introducing Einstein Fields, a neural representation that compresses these simulations into compact implicit neural network weights, enabling the derivation of physical quantities via automatic differentiation and showing potential in continuum modeling, storage efficiency, and derivative accuracy across canonical test beds.
We introduce Einstein Fields, a neural representation that is designed to compress computationally intensive four-dimensional numerical relativity simulations into compact implicit neural network weights. By modeling the \emph{metric}, which is the core tensor field of general relativity, Einstein Fields enable the derivation of physical quantities via automatic differentiation. However, unlike conventional neural fields (e.g., signed distance, occupancy, or radiance fields), Einstein Fields are \emph{Neural Tensor Fields} with the key difference that when encoding the spacetime geometry of general relativity into neural field representations, dynamics emerge naturally as a byproduct. Einstein Fields show remarkable potential, including continuum modeling of 4D spacetime, mesh-agnosticity, storage efficiency, derivative accuracy, and ease of use. We address these challenges across several canonical test beds of general relativity and release an open source JAX-based library, paving the way for more scalable and expressive approaches to numerical relativity. Code is made available at https://github.com/AndreiB137/EinFields