论文标题
快速的半差异最佳运输算法，用于对早期宇宙的独特重建
A fast semi-discrete optimal transport algorithm for a unique reconstruction of the early Universe
论文作者
论文摘要
我们利用最佳传输理论的强大数学工具，并将其转换为有效的算法，以重建原始密度场的波动，构建在求解Monge-Ampère-Kantorovich方程式上。我们的算法计算了一个初始均匀连续密度场（分隔为laguerre单元格）和最终输入的离散点质量集之间的最佳传输，并将早期连接到后期的宇宙。尽管基于完全离散的组合方法的现有早期宇宙重建算法限制为数十万点，但我们的算法扩大了超出此限制的范围，因为它采用了使用牛顿方法解决的良好的平滑凸优化问题的形式。我们从Abacuscosmos Suite运行了有关宇宙学$ n $ body模拟的算法，并通过现成的个人计算机在几个小时内重建$ \ Mathcal {O}（10^7）$粒子的初始位置。我们表明，我们的方法允许对初始功率谱的微妙特征（例如Baryonic声学振荡）进行独特，快速，精确的恢复。
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-Ampère-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 $\mathcal{O}(10^7)$ 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.
