Field-Level Inference

Current-generation galaxy surveys such as DESI, Euclid, and the Rubin Observatory's LSST probe the Large Scale structure (LSS) of the Universe by mapping the spatial distribution of galaxies across the Universe, providing direct observational signatures of evolved primordial fluctuations. The standard analysis approach compresses these maps into summary statistics (power spectrum, bispectrum, etc.), marginalizes over initial conditions, and constrains cosmological parameters.

Field-Level Inference (FLI) takes a different path by forward-modeling end-to-end the Universe 3D or spherical fields (discretized typically into 10⁶ to 10⁹ pixels), from primordial fluctuations through dynamical evolution to survey observables. By performing Bayesian inference directly on such field-level model, FLI avoids lossy compression and extracts the maximum cosmological information encoded in the survey data at a given resolution. As a byproduct, it produces a probabilistic reconstruction of the Universe's history: a digital twin of structure formation that makes dark matter visible and exposes potential modeling systematics.

Ingredients:
Differentiable Models and High-Dimensional Samplers

Field-level inference shifts the challenge from performing analytical or variational marginalization to solving a million to billion-dimensional sampling problem. To make this tractable, we build fast, differentiable simulators using automatic differentiation.

We then invert them with advanced gradient-based sampling methods like MicroCanonical Hamiltonian Monte Carlo. We can also rely on analytic or automatic preconditioning of the sample space.

Application to Weak Lensing 

Weak lensing is a weak regime of gravitational lensing, where light from source galaxies is deflected by the masses neighboring its path, causing galaxies to appear slightly distorted. We can model this phenomena at the field-level by computing the path of the light rays across the simulated cosmic web. We can also incorporate the effect of baryonic physics and the intrinsic alignment of galaxies along the tidal fields.

Application to Galaxy Clustering

Galaxy redshift surveys like DESI and Euclid are powerful probes of the 3D distribution and evolution of matter in the Universe, which depend on properties of dark energy and primordial inflation physics. By modeling dependencies directly at the field-level, we can characterize these properties along with reconstructing the Universe initial conditions.