Emulating Cosmic Structure Formation with a Lagrangian Neural Cellular Automaton
Abstract
Field-level inference of cosmological initial conditions from galaxy surveys requires a forward model that is simultaneously accurate in the non-linear regime, computationally efficient, and fully differentiable. Traditional N-body simulations are accurate but computationally prohibitive for iterative inference, while approximate solvers like Lagrangian Perturbation Theory (LPT) fail to capture the knotty halo-forming dynamics of the cosmic web at late times. We introduce the \textit{Lagrangian Neural Cellular Automaton} (LNCA), a hybrid deep learning framework that can be applied to emulate structure formation as a local, iterative dynamical process on a comoving lattice. Unlike convolutional emulators which map fixed grids in a single pass, the LNCA operates in the Lagrangian frame, iteratively advecting the computational graph itself to follow the flow of mass. By training the network to learn only the \textit{residual} displacement corrections to the Zeldovich approximation, we achieve high-fidelity emulation of the non-linear physics while guaranteeing accuracy at large scales. We further constrain our model to produce complete trajectories, not just final states, by adopting an equivariant cellular automaton architecture, which recurrently iterates on its internal states to yield a dynamic history. The resulting update rule acts on a single fixed neighborhood, is translationally and rotationally equivariant, and is integrated over discrete substeps to yield trajectories, making it a differentiable forward model for reconstructing the initial conditions of the universe from lightcone data. We train our model to emulate the real-space matter distributions of a diverse set of N-body simulations from the Quijote suite, for a range of redshifts and cosmologies, given only the initial conditions.
Related
- Statistics of large-scale structure from the transition probability of Lagrangian trajectories
- Linear perturbation theory and structure formation in a Horndeski theory of gravity without dark matter
- Tracing small-scale structure formation through cosmic time with strong gravitational lensing: A case for a next-generation sub-millimetre/millimetre interferometer
- Aletheia : Emulating the halo mass function with evolution mapping
- Aletheia: Emulating the halo mass function with evolution mapping
BibTeX
@misc{jacobus2026emulating,
title = {{Emulating Cosmic Structure Formation with a Lagrangian Neural Cellular Automaton}},
author = {Cooper Jacobus and Beatriz Tucci and Oliver Philcox},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.27320},
eprint = {2607.27320},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.27320},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Emulating Cosmic Structure Formation with a Lagrangian Neural Cellular Automaton
AU - Cooper Jacobus
AU - Beatriz Tucci
AU - Oliver Philcox
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2607.27320
UR - https://arxiv.org/abs/2607.27320
AB - Field-level inference of cosmological initial conditions from galaxy surveys requires a forward model that is simultaneously accurate in the non-linear regime, computationally efficient, and fully differentiable. Traditional N-body simulations are accurate but computationally prohibitive for iterative inference, while approximate solvers like Lagrangian Perturbation Theory (LPT) fail to capture the knotty halo-forming dynamics of the cosmic web at late times. We introduce the \textit{Lagrangian Neural Cellular Automaton} (LNCA), a hybrid deep learning framework that can be applied to emulate structure formation as a local, iterative dynamical process on a comoving lattice. Unlike convolutional emulators which map fixed grids in a single pass, the LNCA operates in the Lagrangian frame, iteratively advecting the computational graph itself to follow the flow of mass. By training the network to learn only the \textit{residual} displacement corrections to the Zeldovich approximation, we achieve high-fidelity emulation of the non-linear physics while guaranteeing accuracy at large scales. We further constrain our model to produce complete trajectories, not just final states, by adopting an equivariant cellular automaton architecture, which recurrently iterates on its internal states to yield a dynamic history. The resulting update rule acts on a single fixed neighborhood, is translationally and rotationally equivariant, and is integrated over discrete substeps to yield trajectories, making it a differentiable forward model for reconstructing the initial conditions of the universe from lightcone data. We train our model to emulate the real-space matter distributions of a diverse set of N-body simulations from the Quijote suite, for a range of redshifts and cosmologies, given only the initial conditions.
ER -