Field-level weak lensing cosmology with $60$ simulations using multifidelity simulation-based inference

Weak gravitational lensing shear and convergence trace the distribution of baryonic and dark matter across space, making them a powerful probe of cosmic structure. Inferring shear and convergence from images is a challenging inverse problem. The prevailing approach to this task estimates shear from weighted averages of galaxy ellipticities, calibrates these estimates to account for systematic biases, and transforms them to reconstruct convergence, a multistage procedure that requires substantial computational resources and meticulous handling of statistical uncertainties. As an alternative, we propose a probabilistic approach to field-level weak lensing inference in which we train a deep neural network to directly map a multiband image to a variational distribution over the underlying tomographic shear and convergence fields. This neural posterior estimation (NPE) procedure implicitly marginalizes over nuisance variables in the cosmological forward model and does not require evaluating the likelihood function. It is also amortized, so it enables rapid posterior inference for astronomical surveys once the neural network is trained. When evaluated on synthetic images from the LSST-DESC DC2 Simulated Sky Survey, NPE produces well-calibrated variational distributions for shear and convergence that are consistent with the ground truth. We describe how maps sampled from these variational distributions could be used in a subsequent simulation-based inference procedure to approximate the posterior distribution over cosmological parameters.

Reconstructing the three-dimensional distribution of dark matter from weak-lensing observations is a central but highly ill-posed inverse problem in cosmology. Unlike standard 3D reconstruction with multiple viewpoints, we observe the universe from a single line of sight, through noisy shape distortions of galaxies with uncertain distances, so meaningful recovery of the 3D matter field requires strong prior assumptions. Existing methods either produce point estimates with handcrafted priors or use neural ensembles for approximate Bayesian uncertainty, and struggle to capture the non-Gaussian, filamentary structure of the cosmic web. With the advent of new high-resolution cosmological simulations, we now have an alternative source of prior knowledge that captures the nonlinear statistics of structure formation with far greater fidelity than analytic prescriptions. We leverage these simulations to build a new dataset $\texttt{Conicus3D}$, which enables us to learn a data-driven diffusion-model prior capturing the full 3D distribution of dark matter structure across cosmic time. Building on recent plug-and-play approaches, we modify a diffusion-based posterior sampling scheme to the 3D weak-lensing setting, combining the learned prior with a differentiable physical forward model. On realistic simulations targeting a modern weak lensing survey, our approach yields substantially improved 2D and 3D reconstruction accuracy over baseline methods. Moreover, it produces posterior samples whose statistics closely track the underlying simulations, while remaining robust to moderate shifts in cosmology.

We perform field-level likelihood-free inference of the matter density parameter $Ω_m$ from simulated galaxy catalogs using machine learning models with differing inductive biases. Using hydrodynamic simulations from CAMELS, we examine how observable choice and architecture govern cosmological information extraction. We consider galaxy positions and line-of-sight peculiar velocities, separately and jointly, and compare permutation-invariant Deep Sets, implemented with either multilayer perceptrons (MLPs) or Kolmogorov-Arnold Networks (KANs), to graph neural networks (GNNs), which explicitly encode spatial relations. We test in-distribution and out-of-distribution (OOD) performance across simulations with different subgrid galaxy-formation prescriptions. Deep Sets infer $Ω_m$ from velocities alone with mean relative errors of approximately $18\%$ in-distribution and $\sim25\%$ OOD, with KANs and MLPs achieving comparable performance. In contrast, the same set-based approach does not yield useful $σ_8$ predictions in either in-distribution or cross-suite tests. Adding positions does not improve Deep Sets, while GNNs infer $Ω_m$ with mean relative errors of about $10\%$ in-distribution and $10$--$17\%$ OOD. These results indicate that peculiar velocities provide the dominant source of $Ω_m$ information for set-based models in this setting, while spatial information is most effectively used by architectures that explicitly encode galaxy-galaxy relations. Because the velocity inputs are exact simulated peculiar velocities, applications to survey data will require validation under realistic velocity-measurement noise, selection effects, and survey geometry.