# Extensive Studies of the Neutron Star Equation of State from the Deep Learning Inference with the Observational Data Augmentation

arXiv: https://arxiv.org/abs/2101.08156 · HTML: https://mlsanity.com/paper/2101.08156/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 111 references that are in the map.
- First posted on arXiv 20 Jan 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Learning and Generalization in Overparameterized Neural Networks, Going Beyond Two Layers](https://mlsanity.com/paper/1811.04918/) (2018)
- [Deep Learning for Real-time Gravitational Wave Detection and Parameter Estimation: Results with Advanced LIGO Data](https://mlsanity.com/paper/1711.03121/) (2017)
- [Deep Neural Networks to Enable Real-time Multimessenger Astrophysics](https://mlsanity.com/paper/1701.00008/) (2016)
- [What is the Machine Learning?](https://mlsanity.com/paper/1709.10106/) (2017)

## Built on by (most cited first, 3 of 3)

- [Physics-Driven Learning for Inverse Problems in Quantum Chromodynamics](https://mlsanity.com/paper/2501.05580/) (2025)
- [Machine Learning in Nuclear Physics](https://mlsanity.com/paper/2112.02309/) (2021)
- [Machine Learning Meets High-Energy Nuclear Physics: From Pattern Recognition to Physics-Integrated Discovery](https://mlsanity.com/paper/2610.12293/) (2026)

## Abstract (arXiv)

We discuss deep learning inference for the neutron star equation of state (EoS) using the real observational data of the mass and the radius. We make a quantitative comparison between the conventional polynomial regression and the neural network approach for the EoS parametrization. For our deep learning method to incorporate uncertainties in observation, we augment the training data with noise fluctuations corresponding to observational uncertainties. Deduced EoSs can accommodate a weak first-order phase transition, and we make a histogram for likely first-order regions. We also find that our observational data augmentation has a byproduct to tame the overfitting behavior. To check the performance improved by the data augmentation, we set up a toy model as the simplest inference problem to recover a double-peaked function and monitor the validation loss. We conclude that the data augmentation could be a useful technique to evade the overfitting without tuning the neural network architecture such as inserting the dropout.