# Inferring Cosmological Parameters with Evidential Physics-Informed Neural Networks

arXiv: https://arxiv.org/abs/2509.24327 · HTML: https://mlsanity.com/paper/2509.24327/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 53 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Builds on (most cited first, 8 of 8)

- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMAP, and PaCMAP for Data Visualization](https://mlsanity.com/paper/2012.04456/) (2020)
- [Assessing Reliability and Challenges of Uncertainty Estimations for Medical Image Segmentation](https://mlsanity.com/paper/1907.03338/) (2019)
- [On a generalization of the Jensen-Shannon divergence and the JS-symmetrization of distances relying on abstract means](https://mlsanity.com/paper/1904.04017/) (2019)
- [Model Comparison of Dark Energy models Using Deep Network](https://mlsanity.com/paper/1907.00568/) (2019)
- [Evidential Physics-Informed Neural Networks for Scientific Discovery](https://mlsanity.com/paper/2509.14568/) (2025)

## Built on by (most cited first, 1 of 1)

- [Ensemble-Based Dirichlet Modeling for Predictive Uncertainty and Selective Classification](https://mlsanity.com/paper/2604.06032/) (2026)

## Abstract (arXiv)

We examine the use of a novel variant of Physics-Informed Neural Networks to predict cosmological parameters from recent supernovae and baryon acoustic oscillations (BAO) datasets. Our machine learning framework generates uncertainty estimates for target variables and the inferred unknown parameters of the underlying PDE descriptions. Built upon a hybrid of the principles of Evidential Deep Learning, Physics-Informed Neural Networks, Bayesian Neural Networks and Gaussian Processes, our model enables learning of the posterior distribution of the unknown PDE parameters through standard gradient-descent based training. We apply our model to an up-to-date BAO dataset (Bousis et al. 2024) calibrated with the CMB-inferred sound horizon, and the Pantheon+ Sne Ia distances (Scolnic et al. 2018), examining the relative effectiveness and mutual consistency among the standard LambdaCDM, wCDM and LambdasCDM models. Unlike previous results arising from the standard approach of minimizing an appropriate chi2 function, the posterior distributions for parameters in various models trained purely on Pantheon+ data were found to be largely contained within the 2σ contours of their counterparts trained on BAO data. Their posterior medians for h0 were within about 2σ of one another, indicating that our machine learning-guided approach provides a different measure of the Hubble tension.