标题： 贝叶斯深度高斯过程用于相关函数数据：宇宙物质功率谱的案例研究 显示英文标题

标题： Bayesian Deep Gaussian Processes for Correlated Functional Data: A Case Study in Cosmological Matter Power Spectra

摘要： 理解我们的宇宙结构和物质分布是一个活跃的研究领域。 随着宇宙学调查的复杂性增加，开发能够高效且有效地预测物质功率谱的模拟器是必不可少的。 我们特别受到Mira-Titan宇宙模拟套件的启发，该套件对于指定的宇宙学参数化（称为“宇宙学”）提供了多种不同精度的响应曲线，包括相关的函数实现。 我们的目标有两个。 首先，我们从所有提供的曲线上估计潜在的真实物质功率谱，并进行适当的不确定性量化（UQ）。 为此，我们提出了一种新颖的贝叶斯深度高斯过程（DGP）分层模型，该模型综合所有模拟信息来估计潜在的物质功率谱，同时提供有效的UQ。 我们的模型将以前关于贝叶斯DGPs的工作从标量响应扩展到了相关函数输出。 其次，我们利用来自不同宇宙学的预测功率谱，以准确预测未观察到的宇宙学的整个物质功率谱。 对于这项任务，我们使用函数谱的基础函数表示来训练一个独立的高斯过程模拟器。 我们的方法在合成练习中表现良好，并且与基准宇宙学模拟器（Cosmic Emu）相比也表现出色。 显示英文摘要

摘要： Understanding the structure of our universe and the distribution of matter is an area of active research. As cosmological surveys grow in complexity, the development of emulators to efficiently and effectively predict matter power spectra is essential. We are particularly motivated by the Mira-Titan Universe simulation suite that, for a specified cosmological parameterization (termed a "cosmology"), provides multiple response curves of various fidelities, including correlated functional realizations. Our objective is two-fold. First, we estimate the underlying true matter power spectra, with appropriate uncertainty quantification (UQ), from all of the provided curves. To this end, we propose a novel Bayesian deep Gaussian process (DGP) hierarchical model which synthesizes all the simulation information to estimate the underlying matter power spectra while providing effective UQ. Our model extends previous work on Bayesian DGPs from scalar responses to correlated functional outputs. Second, we leverage our predicted power spectra from various cosmologies in order to accurately predict the entire matter power spectra for an unobserved cosmology. For this task, we use basis function representations of the functional spectra to train a separate Gaussian process emulator. Our method performs well in synthetic exercises and against the benchmark cosmological emulator (Cosmic Emu).