Einstein Fields: A Neural Perspective To Computational General
  Relativity
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
687902bccc15e42a72b01ad6
Sandeep Suresh Cranganore
687902bccc15e42a72b01ad7
Andrei Bodnar
claimed_verified
2025-07-17T14:59:15.181Z
66bdb0025bdd611f9a008bec
/avatars/468ec3aebcf798bff601583adbc3bf88.svg
Bodnar
user
AndreiB137
687902bccc15e42a72b01ad8
Arturs Berzins
687902bccc15e42a72b01ad9
Johannes Brandstetter
Einstein Fields: A Neural Perspective To Computational General
  Relativity
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
Einstein Fields, a neural tensor field representation, compresses four-dimensional numerical relativity simulations into neural network weights, enabling automatic differentiation and natural emergence of dynamics.
Einstein Fields neural representation implicit neural network metric general relativity neural tensor fields spacetime geometry automatic differentiation numerical relativity JAX-based library