A fast semidiscrete optimal transport algorithm for a unique reconstruction of the early Universe
A fast semidiscrete optimal transport algorithm for a unique reconstruction of the early Universe
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DOI：
10.1093/mnras/stab1676
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发表时间：
2021-07-13
影响因子：
4.8
通讯作者：
von Hausegger, Sebastian
中科院分区：
文献类型：
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作者：
Levy, Bruno;Mohayaee, Roya;von Hausegger, Sebastian
我们利用来自最优输运理论的强大数学工具，并将其转化为一种有效的算法来重建原始密度场的波动，该算法建立在求解Monge-Ampere-Kantorovich方程的基础上。我们的算法计算初始均匀连续密度场之间的最佳传输，划分成拉盖尔细胞，和离散点质量的最终输入集，连接早期到晚期宇宙。虽然现有的早期宇宙重建算法的基础上完全离散的组合方法被限制在几十万点，我们的算法规模远远超过这个限制，因为它采取了一个适定的光滑凸优化问题的形式，使用牛顿法求解。我们在AbacusCosmos套件中的宇宙学N体模拟上运行我们的算法，并在几个小时内用现成的个人计算机重建O（10（7））粒子的初始位置。我们表明，我们的方法允许一个独特的，快速的，和精确的恢复的初始功率谱的微妙功能，如重子声学振荡。
We leverage powerful mathematical tools stemming from optimal transport theory and transform them into an efficient algorithm to reconstruct the fluctuations of the primordial density field, built on solving the Monge-Ampere-Kantorovich equation. Our algorithm computes the optimal transport between an initial uniform continuous density field, partitioned into Laguerre cells, and a final input set of discrete point masses, linking the early to the late Universe. While existing early universe reconstruction algorithms based on fully discrete combinatorial methods are limited to a few hundred thousand points, our algorithm scales up well beyond this limit, since it takes the form of a well-posed smooth convex optimization problem, solved using a Newton method. We run our algorithm on cosmological N-body simulations, from the AbacusCosmos suite, and reconstruct the initial positions of O(10(7)) particles within a few hours with an off-the-shelf personal computer. We show that our method allows a unique, fast, and precise recovery of subtle features of the initial power spectrum, such as the baryonic acoustic oscillations.