BibTeX

@article{2503.13755v2,
Author        = {Anirban Bairagi and Benjamin Wandelt and Francisco Villaescusa-Navarro},
Title         = {How many simulations do we need for simulation-based inference in
  cosmology?},
Eprint        = {2503.13755v2},
ArchivePrefix = {arXiv},
PrimaryClass  = {astro-ph.CO},
Abstract      = {How many simulations do we need to train machine learning methods to extract
information available from summary statistics of the cosmological density
field? Neural methods have shown the potential to extract non-linear
information available from cosmological data. Success depends critically on
having sufficient simulations for training the networks and appropriate network
architectures. In the first detailed convergence study of neural network
training for cosmological inference, we show that currently available
simulation suites, such as the Quijote Latin Hypercube(LH) with 2000
simulations, do not provide sufficient training data for a generic neural
network to reach the optimal regime, even for the dark matter power spectrum,
and in an idealized case. We discover an empirical neural scaling law that
predicts how much information a neural network can extract from a highly
informative summary statistic, the dark matter power spectrum, as a function of
the number of simulations used to train the network, for a wide range of
architectures and hyperparameters. We combine this result with the Cramer-Rao
information bound to forecast the number of training simulations needed for
near-optimal information extraction. To verify our method we created the
largest publicly released simulation data set in cosmology, the Big Sobol
Sequence(BSQ), consisting of 32,768 $\Lambda$CDM n-body simulations uniformly
covering the $\Lambda$CDM parameter space. Our method enables efficient
planning of simulation campaigns for machine learning applications in
cosmology, while the BSQ dataset provides an unprecedented resource for
studying the convergence behavior of neural networks in cosmological parameter
inference. Our results suggest that new large simulation suites or new training
approaches will be necessary to achieve information-optimal parameter inference
from non-linear simulations.},
Year          = {2025},
Month         = {Mar},
Url           = {http://arxiv.org/abs/2503.13755v2},
File          = {2503.13755v2.pdf}
}