Einstein Fields: A Neural Perspective To Computational General
  Relativity
Authors: name: Sandeep Suresh Cranganore, name: Andrei Bodnar, name: Arturs Berzins, name: Johannes Brandstetter

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
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 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