Probabilistic Mapping of Dark Matter by Neural Score Matching
arXiv:2011.08271
Abstract
The Dark Matter present in the Large-Scale Structure of the Universe is invisible, but its presence can be inferred through the small gravitational lensing effect it has on the images of far away galaxies. By measuring this lensing effect on a large number of galaxies it is possible to reconstruct maps of the Dark Matter distribution on the sky. This, however, represents an extremely challenging inverse problem due to missing data and noise dominated measurements. In this work, we present a novel methodology for addressing such inverse problems by combining elements of Bayesian statistics, analytic physical theory, and a recent class of Deep Generative Models based on Neural Score Matching. This approach allows to do the following: (1) make full use of analytic cosmological theory to constrain the 2pt statistics of the solution, (2) learn from cosmological simulations any differences between this analytic prior and full simulations, and (3) obtain samples from the full Bayesian posterior of the problem for robust Uncertainty Quantification. We present an application of this methodology on the first deep-learning-assisted Dark Matter map reconstruction of the Hubble Space Telescope COSMOS field.
arXiv comment6 pages, accepted submission to the NeurIPS 2019 Machine Learning and the Physical Sciences Workshop
References in corpus (14)
- Variational Inference with Normalizing Flows
- A Conceptual Introduction to Hamiltonian Monte Carlo
- COSMOS : Hubble Space Telescope Observations
- Evidence for the accelerated expansion of the Universe from weak lensing tomography with COSMOS
- Improved Techniques for Training Score-Based Generative Models
- MassiveNuS: Cosmological Massive Neutrino Simulations
- Wiener Reconstruction of Galaxy Surveys in Spherical Harmonics
- Hierarchical Cosmic Shear Power Spectrum Inference
- Cosmological parameters, shear maps and power spectra from CFHTLenS using Bayesian hierarchical inference
- Deep learning dark matter map reconstructions from DES SV weak lensing data
- High Resolution Weak Lensing Mass-Mapping Combining Shear and Flexion
- Improving Weak Lensing Mass Map Reconstructions using Gaussian and Sparsity Priors: Application to DES SV
- Denoising Weak Lensing Mass Maps with Deep Learning
- Sparse Bayesian mass-mapping with uncertainties: local credible intervals