Replicating weak-lensing summary-statistic covariances with normalizing flows
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| Format: | Preprint |
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2026
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| _version_ | 1866915759556395008 |
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| author | Armijo, Joaquin Thiele, Leander Liu, Jia |
| author_facet | Armijo, Joaquin Thiele, Leander Liu, Jia |
| contents | We explore the ability of normalizing flow (NF) generative models to reproduce weak-lensing summary statistics when trained on a set of cosmological simulations. Our analysis focuses on how accurately NF models recover the mean, standard deviation, and covariance of key statistics derived from convergence ($κ$) maps: The angular power spectrum $C_{\ell}$, probability density function, and Minkowski functionals of weak lensing convergence $κ$-maps. We test two scenarios for training: (1) on the data vectors and (2) on the full $κ$-maps. In both cases, the NF models reproduce the mean and variance of the target statistics within percent-level accuracy. However, the accuracy of the off-diagonal elements of the covariance matrix is underestimated by up to $\sim25\%$. We study several mitigation strategies and find that data augmentation and training with noisy fields help improve covariance recovery to $\mathcal{O}(10\%)$. Our study demonstrates that while the means and variances of weak lensing statistics can be well modeled by NF, covariances can be significantly underestimated if mitigation strategies are not applied. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_20669 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Replicating weak-lensing summary-statistic covariances with normalizing flows Armijo, Joaquin Thiele, Leander Liu, Jia Cosmology and Nongalactic Astrophysics We explore the ability of normalizing flow (NF) generative models to reproduce weak-lensing summary statistics when trained on a set of cosmological simulations. Our analysis focuses on how accurately NF models recover the mean, standard deviation, and covariance of key statistics derived from convergence ($κ$) maps: The angular power spectrum $C_{\ell}$, probability density function, and Minkowski functionals of weak lensing convergence $κ$-maps. We test two scenarios for training: (1) on the data vectors and (2) on the full $κ$-maps. In both cases, the NF models reproduce the mean and variance of the target statistics within percent-level accuracy. However, the accuracy of the off-diagonal elements of the covariance matrix is underestimated by up to $\sim25\%$. We study several mitigation strategies and find that data augmentation and training with noisy fields help improve covariance recovery to $\mathcal{O}(10\%)$. Our study demonstrates that while the means and variances of weak lensing statistics can be well modeled by NF, covariances can be significantly underestimated if mitigation strategies are not applied. |
| title | Replicating weak-lensing summary-statistic covariances with normalizing flows |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2601.20669 |