# Constraining cosmological parameters from N-body simulations with Variational Bayesian Neural Networks

arXiv: https://arxiv.org/abs/2301.03991 · HTML: https://mlsanity.com/paper/2301.03991/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 46 references that are in the map.
- First posted on arXiv 9 Jan 2023.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [Why Normalizing Flows Fail to Detect Out-of-Distribution Data](https://mlsanity.com/paper/2006.08545/) (2020)
- [Multiplicative Normalizing Flows for Variational Bayesian Neural Networks](https://mlsanity.com/paper/1703.01961/) (2017)
- [Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches](https://mlsanity.com/paper/1803.04386/) (2018)
- [Hierarchical Variational Models](https://mlsanity.com/paper/1511.02386/) (2015)
- [Randomized Value Functions via Multiplicative Normalizing Flows](https://mlsanity.com/paper/1806.02315/) (2018)
- [Estimating Cosmological Parameters from the Dark Matter Distribution](https://mlsanity.com/paper/1711.02033/) (2017)
- [Hierarchical Inference With Bayesian Neural Networks: An Application to Strong Gravitational Lensing](https://mlsanity.com/paper/2010.13787/) (2020)
- [3D Convolutional Neural Networks for Stalled Brain Capillary Detection](https://mlsanity.com/paper/2104.01687/) (2021)
- [Parameters Estimation for the Cosmic Microwave Background with Bayesian Neural Networks](https://mlsanity.com/paper/1911.08508/) (2019)
- [Bayesian Neural Networks: Essentials](https://mlsanity.com/paper/2106.13594/) (2021)
- [Machine Learning and Cosmology](https://mlsanity.com/paper/2203.08056/) (2022)
- [Constraining the Reionization History using Bayesian Normalizing Flows](https://mlsanity.com/paper/2005.07694/) (2020)
- [Constraining cosmological parameters from N-body simulations with Bayesian Neural Networks](https://mlsanity.com/paper/2112.11865/) (2021)

## Built on by (most cited first, 2 of 2)

- [Forecasting VIX using Bayesian Deep Learning](https://mlsanity.com/paper/2401.17042/) (2024)
- [Cosmology with Persistent Homology: Parameter Inference via Machine Learning](https://mlsanity.com/paper/2412.15405/) (2024)

## Abstract (arXiv)

Methods based on Deep Learning have recently been applied on astrophysical parameter recovery thanks to their ability to capture information from complex data. One of these methods is the approximate Bayesian Neural Networks (BNNs) which have demonstrated to yield consistent posterior distribution into the parameter space, helpful for uncertainty quantification. However, as any modern neural networks, they tend to produce overly confident uncertainty estimates and can introduce bias when BNNs are applied to data. In this work, we implement multiplicative normalizing flows (MNFs), a family of approximate posteriors for the parameters of BNNs with the purpose of enhancing the flexibility of the variational posterior distribution, to extract Omegam, h, and σ8 from the QUIJOTE simulations. We have compared this method with respect to the standard BNNs, and the flipout estimator. We found that MNFs combined with BNNs outperform the other models obtaining predictive performance with almost one order of magnitude larger that standard BNNs, σ8 extracted with high accuracy (r2=0.99), and precise uncertainty estimates. The latter implies that MNFs provide more realistic predictive distribution closer to the true posterior mitigating the bias introduced by the variational approximation and allowing to work with well-calibrated networks.