Bayesian emulator optimisation for cosmology: application to the Lyman-alpha forest
Bayesian emulator optimisation for cosmology: application to the Lyman-alpha forest
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DOI：
10.1088/1475-7516/2019/02/031
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发表时间：
2018-12
影响因子：
6.4
通讯作者：
K. Rogers;H. Peiris;A. Pontzen;Simeon Bird;L. Verde;A. Font-Ribera
中科院分区：
文献类型：
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作者：
K. Rogers;H. Peiris;A. Pontzen;Simeon Bird;L. Verde;A. Font-Ribera
莱曼-阿尔法森林对宇宙学参数和星系际介质天体物理学都提供了强有力的约束，预计下一代的调查，包括eBOSS和DESI，将进一步改善。在宇宙学推断中，提取这些信息需要在整个高维参数空间中计算可能性。评估的可能性需要一个强大的和准确的参数和观测值之间的映射，在这种情况下，1D通量功率谱。宇宙学模拟使这样的映射成为可能，但由于计算时间的限制，只能在少数几个样本点上进行评估;“仿真器”被设计成在这些样本点之间进行插值。然后，问题简化为放置样本点，以便获得准确的映射，同时最大限度地减少所需的昂贵模拟的数量。为了解决这个问题，我们引入了一个仿真程序，采用贝叶斯优化的训练集的高斯过程插值方案。从拉丁超立方体采样开始（可以使用具有良好空间填充特性的其他方案），我们在新的参数位置上使用额外的模拟来迭代地增加训练集，这些参数位置平衡了减少插值误差的需要，同时专注于高可能性区域。我们发现，较小的仿真器误差从贝叶斯优化传播到较小的宽度后验分布。即使比拉丁超立方体更少的模拟，贝叶斯优化也将95%的可信体积缩小了90%，例如，小尺度原始波动振幅的1σ误差为38%。这是贝叶斯优化应用于大规模结构仿真的第一次演示，我们预计该技术将推广到许多其他探测器，如星系聚类，弱透镜和21厘米。
The Lyman-alpha forest provides strong constraints on both cosmological parameters and intergalactic medium astrophysics, which are forecast to improve further with the next generation of surveys including eBOSS and DESI. As is generic in cosmological inference, extracting this information requires a likelihood to be computed throughout a high-dimensional parameter space. Evaluating the likelihood requires a robust and accurate mapping between the parameters and observables, in this case the 1D flux power spectrum. Cosmological simulations enable such a mapping, but due to computational time constraints can only be evaluated at a handful of sample points; “emulators” are designed to interpolate between these. The problem then reduces to placing the sample points such that an accurate mapping is obtained while minimising the number of expensive simulations required. To address this, we introduce an emulation procedure that employs Bayesian optimisation of the training set for a Gaussian process interpolation scheme. Starting with a Latin hypercube sampling (other schemes with good space-filling properties can be used), we iteratively augment the training set with extra simulations at new parameter positions which balance the need to reduce interpolation error while focussing on regions of high likelihood. We show that smaller emulator error from the Bayesian optimisation propagates to smaller widths on the posterior distribution. Even with fewer simulations than a Latin hypercube, Bayesian optimisation shrinks the 95% credible volume by 90% and, e.g., the 1σ error on the amplitude of small-scale primordial fluctuations by 38%. This is the first demonstration of Bayesian optimisation applied to large-scale structure emulation, and we anticipate the technique will generalise to many other probes such as galaxy clustering, weak lensing and 21cm.