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 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).

翻译：理解宇宙结构及物质分布是当前活跃的研究领域。随着宇宙学巡天观测的日益复杂，开发高效且精准的模拟器来预测物质功率谱变得至关重要。本研究尤其受到Mira-Titan宇宙模拟套件的驱动，该套件针对特定宇宙学参数化（即"宇宙学模型"），能够提供多条不同保真度的响应曲线，包括相关的函数化实现。我们的目标具有双重性：首先，根据提供的所有曲线，在适当的量化不确定度条件下估计潜在的宇宙物质功率谱。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以估计物质功率谱，同时提供有效的不确定度量化。本模型将先前关于贝叶斯DGP的研究从标量响应扩展至相关函数型输出。其次，我们利用基于不同宇宙学模型预测的功率谱，准确预测未观测宇宙学模型的完整功率谱。对于该任务，我们采用函数谱的基函数表示来训练独立的DGP模拟器。本方法在合成测试中表现优异，并优于基准宇宙学模拟器（Cosmic Emu）。