Cosmological probes pose an inverse problem where the measurement result is obtained through observations, and the objective is to infer values of model parameters that characterize the underlying physical system—our universe, from these observations and theoretical forward-modeling. The only way to accurately forward-model physical behavior on small scales is via expensive numerical simulations, which are further “emulated” due to their high cost. Emulators are commonly built with a set of simulations covering the parameter space with Latin hypercube sampling and an interpolation procedure; the aim is to establish an approximately constant prediction error across the hypercube. In this paper, we provide a description of a novel statistical framework for obtaining accurate parameter constraints. The proposed framework uses multi-output Gaussian process emulators that are adaptively constructed using Bayesian optimization methods with the goal of maintaining a low emulation error in the region of the hypercube preferred by the observational data. In this paper, we compare several approaches for constructing multi-output emulators that enable us to take possible inter-output correlations into account while maintaining the efficiency needed for inference. Using a Lyα forest flux power spectrum, we demonstrate that our adaptive approach requires considerably fewer—by a factor of a few in the LyαP(k) case considered here—simulations compared to the emulation based on Latin hypercube sampling, and that the method is more robust in reconstructing parameters and their Bayesian credible intervals.

宇宙学探针提出了一个反问题，即通过观测获得测量结果，目的是从这些观测和理论正演模型中推断出表征基础物理系统（我们的宇宙）的模型参数的值。准确地在小规模上对物理行为进行正向建模的唯一方法是通过昂贵的数值模拟，由于成本高昂，这些模拟被进一步“模拟”。仿真器通常是通过使用拉丁美洲超立方体采样和插值过程覆盖参数空间的一组仿真来构建的；目的是在超立方体上建立近似恒定的预测误差。在本文中，我们提供了一种用于获取准确参数约束的新型统计框架的描述。所提出的框架使用多输出高斯过程仿真器，该仿真器是使用贝叶斯优化方法自适应构建的，目的是在观测数据首选的超立方体区域中保持低仿真误差。在本文中，我们比较了构造多输出仿真器的几种方法，这些方法使我们能够将可能的输出间相关性考虑在内，同时保持推理所需的效率。使用Ly 我们比较了构建多输出仿真器的几种方法，这些方法使我们能够将可能的输出间相关性考虑在内，同时保持推理所需的效率。使用Ly 我们比较了构建多输出仿真器的几种方法，这些方法使我们能够将可能的输出间相关性考虑在内，同时保持推理所需的效率。使用Lyα森林通量功率谱，我们证明，我们的自适应方法需要相当少的，由少数的在Ly的一个因子α P（ķ与基于拉丁超立方采样仿真考虑）的情况下在这里的仿真，并且，该方法是在重建参数及其贝叶斯可信区间方面更强大。