Details

Autor(en) / Beteiligte

• Levy, Bruno
• Mohayaee, Roya
• von Hausegger, Sebastian

Titel

A fast semidiscrete optimal transport algorithm for a unique reconstruction of the early Universe

Ist Teil von

• Monthly notices of the Royal Astronomical Society, 2021-09, Vol.506 (1), p.1165-1185

Ort / Verlag

Oxford University Press (OUP): Policy P - Oxford Open Option A

Erscheinungsjahr

2021

Link zum Volltext

Quelle

Free E-Journal (出版社公開部分のみ）

Beschreibungen/Notizen

• ABSTRACT 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.