标题： 基于物理学驱动机器学习的线性物质功率谱分析仿真器 显示英文标题

标题： Analytical Emulator for the Linear Matter Power Spectrum from Physics-Informed Machine Learning

摘要： 当前和未来的星系大尺度结构巡天旨在通过分析海量数据，以前所未有的精度限制宇宙学参数。这就迫切需要开发快速且准确的方法来计算物质功率谱$P(k)$，或者等效地，物质传递函数$T(k)$。 在之前的工作中，我们在标准宇宙学模型内引入了这些量的精确拟合公式，包括具有大质量中微子和引力修正等扩展内容。 然而，这些公式忽略了在$P(k)$中留下的一个关键特征：声波振荡信号。 在这里，我们利用对这种振荡模式背后已知物理知识的理解，对我们的遗传算法（一种机器学习技术）施加约束。 通过采用这种“基于物理”方法，我们提出了一种表达式，能够以小于百分之一的平均误差准确描述物质传递函数。 输出的高度可解释性使得这种公式的简单扩展成为可能，适用于涉及大质量中微子和引力修正的其他场景。 我们预计，此公式将成为$P(k)$的竞争性拟合函数，满足宇宙学分析所需的精度要求。 显示英文摘要

摘要： Current and future large-scale structure surveys aim to constrain cosmological parameters with unprecedented precision by analyzing vast amounts of data. This imposes a pressing need to develop fast and accurate methods for computing the matter power spectrum $P(k)$, or equivalently, the matter transfer function $T(k)$. In previous works, we introduced precise fitting formulas for these quantities within the standard cosmological model, including extensions such as the presence of massive neutrinos and modifications of gravity. However, these formulations overlooked a key characteristic imprinted in $P(k)$: the baryon acoustic oscillation signal. Here, we leverage our understanding of the well-known physics behind this oscillatory pattern to impose constraints on our genetic algorithm, a machine learning technique. By employing this ``physics-informed'' approach, we introduce an expression that accurately describes the matter transfer function with sub-percent mean accuracy. The high interpretability of the output allows for straightforward extensions of this formulation to other scenarios involving massive neutrinos and modifications of gravity. We anticipate that this formula will serve as a competitive fitting function for $P(k)$, meeting the accuracy requirements essential for cosmological analyses.