[论文解读] A field-level emulator for modified gravity

Daniela Saadeh, K. Koyama+1 more|arXiv (Cornell University)|Jun 5, 2024

Geophysics and Gravity Measurements被引用 4

一句话总结

该论文提出了一种场级神经网络模拟器，可将ΛCDM N体模拟结果转换为等效的f(R)修正引力模拟结果，以引力强度|f_R0|作为风格条件。在固定宇宙学参数下进行训练，其在k ~ 1 h/Mpc以内非线性物质功率谱上的精度达到1%，并展现出对未见宇宙学参数的强大外推性能。

ABSTRACT

Stage IV surveys like LSST and Euclid present a unique opportunity to shed light on the nature of dark energy. However, their full constraining power cannot be unlocked unless accurate predictions are available at all observable scales. Currently, only the linear regime is well understood in models beyond $Λ$CDM: on the nonlinear scales, expensive numerical simulations become necessary, whose direct use is impractical in the analyses of large datasets. Recently, machine learning techniques have shown the potential to break this impasse: by training emulators, we can predict complex data fields in a fraction of the time it takes to produce them. In this work, we present a field-level emulator capable of turning a $Λ$CDM N-body simulation into one evolved under $f(R)$ gravity. To achieve this, we build on the map2map neural network, using the strength of modified gravity $|f_{R_0}|$ as style parameter. We find that our emulator correctly estimates the changes it needs to apply to the positions and velocities of the input N-body particles to produce the target simulation. We test the performance of our network against several summary statistics, finding $1\%$ agreement in the power spectrum up to $k \sim 1$ $h/$Mpc, and $1.5\%$ agreement against the independent boost emulator eMantis. Although the algorithm is trained on fixed cosmological parameters, we find it can extrapolate to models it was not trained on. Coupled with available field-level emulators and simulation suites for $Λ$CDM, our algorithm can be used to constrain modified gravity in the large-scale structure using full information available at the field level.

研究动机与目标

• 为克服在不同宇宙学参数下对f(R)等修正引力模型运行完整N体模拟所面临的计算成本。
• 通过保留总结统计量中丢失的相位和形态信息，实现在大尺度结构宇宙学中的场级推断。
• 开发一种可微分、可泛化的模拟器，能够外推至其训练宇宙学参数之外，以加速宇宙学模型测试。
• 与现有的ΛCDM场级模拟器（如map2map）集成，实现在未来第四阶段巡天中对修正引力的端到端、高保真度测试。
• 通过提供修正引力下物质场和速度场的准确、快速预测，支持BORG等先进推断框架。

提出的方法

• 将map2map神经网络架构适配为场级模拟器，将ΛCDM粒子位置和速度映射为其在f(R)引力下的对应场。
• 使用f(R)参数的绝对值|f_R0|作为风格嵌入，以条件化网络对输入N体场的变换。
• 在一组固定宇宙学参数（ΩM, σ8, h等）但不同|f_R0|值的ΛCDM模拟上进行模型训练。
• 采用损失函数，最小化关键宇宙学统计量之间的差异：功率谱、三体谱、密度场和动量场，以及红移空间扭曲。
• 通过ECOSMOG自适应网格细化（AMR）代码生成的独立模拟验证性能，并与eMantis模拟器在增益因子精度上进行比较。
• 通过零样本外推至训练集中未包含的宇宙学参数（包括ΩM、σ8和h的极端值）评估泛化能力。

Figure 1: Comparison of the emulator’s output against the target snapshot. In this example, $|f_{R_{0}}|$ $=10^{-5}$ . The top, middle, and bottom rows show the projected density field reconstructed from the snapshots, along three perpendicular directions. The left and middle columns show the emulat

实验结果

研究问题

• RQ1 深度学习模拟器能否在场级准确地将ΛCDM N体模拟转换为f(R)引力模拟，同时保留幅度和相位信息？
• RQ2 此类模拟器在训练分布之外的宇宙学参数（特别是ΩM、σ8和h）上能多大程度上实现泛化？
• RQ3 模拟器在多大程度上能准确再现关键可观测量，如非线性物质功率谱、三体谱和红移空间扭曲？
• RQ4 模拟器能否在第四阶段巡天相关尺度范围（k < 1 h/Mpc）内实现总结统计量的亚百分之一精度？
• RQ5 与eMantis等成熟模拟器相比，该模拟器在预测增长速率增益因子方面的性能如何？

主要发现

• 该模拟器在k ~ 1 h/Mpc以内，非线性物质功率谱与目标模拟结果的差异达到1%以内。
• 在相同尺度范围内，其在增益因子上的表现与独立的eMantis模拟器相比误差不超过1.5%。
• 模拟器对三体谱的再现精度约为1%，表明其成功保留了相位和形态结构。
• 在k < 0.3 h/Mpc的尺度上，红移空间扭曲的一阶和二阶矩预测与目标模拟结果的差异在4%以内。
• 在k < 1 h/Mpc和k < 0.3 h/Mpc的尺度上，模拟密度场和动量场的随机性分别低于0.4%。
• 该模型在未见宇宙学参数上表现出良好的泛化能力，在不同ΩM、σ8和h值下，增益因子精度达到约3%，三体谱精度达到约1.5%。

Figure 2: Relative error on the boost factor ${P(k)}^{\mathrm{(MG)}}/{P(k)}^{\mathrm{(\Lambda CDM)}}$ as computed from the 2000 FML simulations in the traning, validation and test datasets, and using the screening efficiencies listed in Table 1 . For this comparison, we use eMantis as the ground tru