Extensive studies of the neutron star equation of state from the deep learning inference with the observational data augmentation

Abstract

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.

Translating Neutron Star Observations to Nuclear Symmetry Energy via Deep Neural Networks

“…At asymptotically high densities of ρ 50 ρ 0 , perturbative QCD calculations converge and provide reliable results [51][52][53][54][55][56][57]. At intermediate densities of ρ ∼ [2 − 10]ρ 0 , however, there are still no reliable QCD predictions [58]. To derive the EOS from QCD in the intermediatedensity region, one needs to develop non-perturbative approaches, such as the Monte Carlo simulation of QCD on a lattice (lattice QCD), but the application of these methods to systems at finite densities is hindered by the notorious sign problem; see, e.g., Ref.…”

Translating neutron star observations to nuclear symmetry energy via artificial neural networks

“…At asymptotically high densities of ρ > ∼ 50ρ 0 perturbative QCD calculations converge and provide reliable results [51][52][53][54][55][56][57]. At intermediate densities of ρ ∼ [2 − 10]ρ 0 , however, there are still no reliable QCD predictions [58]. To derive the EOS from QCD in the intermediate density region, one needs to develop non-perturbative approaches, such as the Monte-Carlo simulation of QCD on a lattice (lattice QCD), but the application of these methods to systems at finite densities is hindered by the notorious sign problem, see, e.g.…”

“…[85]. Despite the significant effort to extract the genuine EOS from the NS astrophysical data, it is still unclear what the true dense matter EOS should look like mainly due to the uncertainties of the assumed prior distributions in the Bayesian analyses [58]. Therefore, the need arises of alternative approaches to construct the model independent EOS.…”

“…In previous works [125,126], we also pioneered the use of DL methods, specifically Convolutional Neural Network (CNN) [127] algorithms, for detection and inference of GW signals from binary neutron star (BNS) mergers embedded in both Gaussian and realistic LIGO noise. Several studies have also explored the DL approach as a tool to extract the dense matter EOS from NS observations [58,[128][129][130][131].…”

Applications of deep learning in high energy nuclear physics

“…价于一个矩阵， 只具备线性表示能力。 理论证明， 只 要输入层与输出层之间添加一个隐藏层，再加上非 线性激活函数，原则上就可以用有限但足够数量的 神经元无限逼近任意的连续实函数 [10][11] 。这个定 理被称为通用近似定理 (Universal approximation theorem)，它使得我们可以针对不同的问题和数据 结构， 设计相应的人工神经网络， 解决比如分类、 回 归、聚类、非线性特征降维等等复杂的问题。 Bias 输⼊层 隐藏层 输出层 图 1 包含一个隐藏层的人工神经网络的示例 通常来说，我们可以将机器学习处理问题的 方法分成三类：监督学习，无监督学习和强化学 习 [3][4] 1) 。它们之间的差异来自人对机器学习过程 的干预程度不同：监督学习需要给定训练中输入数 据的标签作为监督指导；而无监督学习是机器从数 据自行挖掘其中的模式规律；强化学习则是设定反 馈 (reward) 机制，通过奖励和惩罚来训练智能体 (agent) 对环境的响应。几种方式各有所长，例如监 督学习在图像分类和文本理解等分类回归问题上表 现出色， 无监督学习适用于异常检测、 推荐系统、 大 数据可视化等聚类降维问题， 而强化学习在游戏 AI 以及天气预报等实时决策问题中大放异彩 [4][5] 。基 于以上的成功应用场景，这些新型建模和数据处理 方法正在物理科学研究的各个尺度上大展身手：从 在数万亿天空像素中寻找系外行星，到利用大尺度 结构观测推测宇宙常数，再到在大型强子对撞机事 件中探测信号等 [8,[14][15] 。 此外， 从计算物理角度， 原 有的计算模拟加速效率、优化反问题求解和革新第 一性原理计算技术等等目标也因机器学习社区的蓬 勃发展而受益 [6,[16][17] 。除了使用机器学习方法进行 科学发现和改进计算外，也有超出应用范畴对机器 学习模型进行物理可解释性的探索，比如探讨深度 神经网络提取数据特征和重整化方法的等价性、尝 试直接引入物理规律来改进机器学习性能等 [18][19] 。 以上种种应用和成果同时也在深远地影响着分子动 力学、药物设计、材料设计、成像系统优化和金融 系统分析等与产业结合更紧密的领域 [6,[20][21] 。 在高能核物理领域，由于实验数据量大、模拟 计算需求大和第一性原理计算开销大的特点，深度 学习已经成为必不可少的技术。目前已在如下几个 方面有广泛应用： 探测器设计、 粒子重建和分析、 喷 柱 (Jet) 分类等 [14,[22][23] ；物理模拟的加速、对物态 或物理过程信息的提取等 [24][25][26][27] ；对物理表征方式 的优化、第一性原理计算加速等 [28][29][30][31] ；以及对核天 体物理观测的处理和物态性质的研究 [32][33][34] 。 本文立 足于作者最近的系列工作和新进展，管中窥豹，试 图从相对论重离子碰撞和格点 QCD 计算两个方向 的相关研究出发，简要阐述深度学习在关键物理信 息重建、计算性能改进等方面的应用。 1) 或者按另一种分法，分成判别式学习和生成式学习，后者以表征数据背后的概率分布为核心。除此之外，还发展出了半监督学习、自监督 学习、对比学习以及主动学习等弱监督式的方法 [12][13]…”