# Field-Level Inference with Microcanonical Langevin Monte Carlo

arXiv: https://arxiv.org/abs/2307.09504 · HTML: https://mlsanity.com/paper/2307.09504/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2023.

## Built on by (most cited first, 5 of 5)

- [MadEvolve: Evolutionary Optimization of Cosmological Algorithms with Large Language Models](https://mlsanity.com/paper/2602.15951/) (2026)
- [Symmetry Breaking in Transformers for Efficient and Interpretable Training](https://mlsanity.com/paper/2601.22257/) (2026)
- [CosmoBench: A Multiscale, Multiview, Multitask Cosmology Benchmark for Geometric Deep Learning](https://mlsanity.com/paper/2507.03707/) (2025)
- [Initial Conditions from Galaxies: Machine-Learning Subgrid Correction to Standard Reconstruction](https://mlsanity.com/paper/2504.01092/) (2025)
- [Microcanonical Hamiltonian Monte Carlo and the Helmholtz Theorem](https://mlsanity.com/paper/2609.07620/) (2026)

## Abstract (arXiv)

Field-level inference provides a means to optimally extract information from upcoming cosmological surveys, but requires efficient sampling of a high-dimensional parameter space. This work applies Microcanonical Langevin Monte Carlo (MCLMC) to sample the initial conditions of the Universe, as well as the cosmological parameters σ8 and Omegam, from simulations of cosmic structure. MCLMC is shown to be over an order of magnitude more efficient than traditional Hamiltonian Monte Carlo (HMC) for a ~ 2.6 × 105 dimensional problem. Moreover, the efficiency of MCLMC compared to HMC greatly increases as the dimensionality increases, suggesting gains of many orders of magnitude for the dimensionalities required by upcoming cosmological surveys.