# Reconstruction papers

Here I collect papers related to reconstruction of the initial conditions. I try to include all, but probably have missed some. Please kindly send me a message if you notice I should include something.

## Machine learning based methods

Legin, R., et al., "Posterior Sampling of the Initial Conditions of the Universe from Non-linear Large Scale Structures using Score-Based Generative Models", 2023 (ADS)

Generative model

Chen, X., Zhu, F., Gaines, S., & Padmanabhan, N., "Effective cosmic density field reconstruction with convolutional neural network", 2023 (ADS)

CNN+traditional algorithm

Jindal, V., et al., "Predicting the Initial Conditions of the Universe using Deep Learning", 2023 (ADS)

V-Net

Shallue, C. J., & Eisenstein, D. J., "Reconstructing cosmological initial conditions from late-time structure with convolutional neural networks", 2023 (ADS)

CNN+traditional algorithm

Mao, T.-X., "Baryon acoustic oscillations reconstruction using convolutional neural networks", 2021 (ADS)

CNN, real space

Alves de Oliveira, R., et al., "Fast and Accurate Non-Linear Predictions of Universes with Deep Learning" 2020 (ADS)

V-Net

## Traditional algorithms

Nikakhtar, F., et al., "Optimal Transport Reconstruction of Biased Tracers in Redshift Space", 2023 (ADS)

Optimal transport reconstruction on biased tracers

Seo, H., et al., "Iterative reconstruction excursions for Baryon Acoustic Oscillations and beyond", 2022 (ADS)

A few iterative schemes

Nikakhtar, F., Sheth, R. K., Levy, B., & Mohayaee, R., "Optimal Transport Reconstruction of Baryon Acoustic Oscillations", 2022 (ADS)

Optimal transport

von Hausegger, S., Levy, B., & Mohayaee, R., "Accurate Baryon Acoustic Oscillations Reconstruction via Semidiscrete Optimal Transport", 2022 (ADS)

Optimal transport reconstruction on 1D BAO parameter recovery

Levy, B., Mohayaee R., & von Hausegger, S., "A fast semidiscrete optimal transport algorithm for a unique reconstruction of the early Universe", 2021 (ADS)

Optimal transport

Nikakhtar, F., Sheth, & R. K., Zehavi, I., "Laguerre reconstruction of the BAO feature in halo-based mock galaxy catalogues", 2021 (ADS)

Application of Laguerre reconstruction in galaxy fields

Nikakhtar, F., Sheth, & R. K., Zehavi, I., "Laguerre reconstruction of the correlation function on baryon acoustic oscillation scales", 2021 (ADS)

Reconstruction of two-point correlation function using Laguerre functions

Chen, X. & Padmanabhan, N. "Analysis of an iterative reconstruction method in comparison of the standard reconstruction method", 2023 (ADS)

Detailed analysis of HE18 in comparison of the standard reconstruction method

Hada, R., & Eisenstein, D. J., "Application of the iterative reconstruction to simulated galaxy fields", 2019 (ADS)

Application of HE18 in galaxy fields

Hada, R., & Eisenstein, D. J., "An iterative reconstruction of cosmological initial density fields", 2018 (ADS)

Iterative algorithm, reconstructs the density field directly w/o moving particles, reconstructs in Lagrangian space, rather than in Eulerian space, annealing smoothing, among other differences from the standard reconstruction algorithm; real & redshift space matter field

Schmittfull, M., Baldauf, T., & Zaldarriaga, M., "Iterative initial condition reconstruction", 2017 (ADS)

Iteratively computes the displacement field working to second order in density field; includes second order as an option, but has marginal improvement.

Obuljen, A., Villaescusa-Navarro, F., Castorina, E., & Viel, M., "Baryon Acoustic Oscillations reconstruction with pixels", 2017 (ADS)

Standard reconstruction with pixels

Zhu, H., et al., "Nonlinear reconstruction", 2017 (ADS)

Nonlinear displacement

Seo, H., & Hirata, C. M., "The foreground wedge and 21-cm BAO surveys", 2016 (ADS)

Standard reconstruction with pixels

Zhu, H., Pen, U., & Chen, X. "Primordial density and BAO reconstruction", 2016 (ADS)

Nonlinear displacement field, 1D

Schmittfull, M. et al, "Eulerian BAO reconstructions and N -point statistics", 2015 (ADS)

Eulerian growth shift; also showed reconstruction moving higher-point statistics to power spectrum

Tassev, S., & Zaldarriaga, M., "Towards an optimal reconstruction of baryon oscillations", 2012 (ADS)

Improvement to the standard reconstruction algorithm, no free parameters, optimal filters

Seo, H., et al., "High-precision predictions for the acoustic scale in the non-linear regime", 2010 (ADS)

Included 2LPT and iterative operations for standard reconstruction algorithm, but found little improvement

Eisenstein, D. J., Seo, H., Sirko, E., & Spergel, D. N., "Improving Cosmological Distance Measurements by Reconstruction of the Baryon Acoustic Peak", 2007 (ADS)

Standard reconstruction algorithm

Brenier, Y., et al., "Reconstruction of the early Universe as a convex optimization problem", 2003 (ADS)

Least action

Monaco, P., & Efstathiou, G., "Reconstruction of cosmological initial conditions from galaxy redshift catalogues", 1999 (ADS)

Self-consistent solution of the growing mode with ZA and LPT; iterative scheme

Narayanan, V. K., & Croft, R. A. C. "Recovering the Primordial Density Fluctuations: A Comparison of Methods", 1999 (ADS)

Comparison of previous methods

Croft, R. A. C., & Gaztanaga, E. "Reconstruction of cosmological density and velocity fields in the Lagrangian Zel'dovich approximation", 1997 (ADS)

Least action

Gramann, M., "An Improved Reconstruction Method for Cosmological Density Fields", 1993 (ADS)

Zel'dovich approximation

Nusser, A., & Dekel, A., "Tracing Large-Scale Fluctuations Back in Time", 1992 (ADS)

Zel'dovich approximation

Weinberg, D. H., "Reconstructing primordial density fluctuations. I - Method", 1992 (ADS)

Gaussianization

Peebles, P. J. E., "The Gravitational Instability Picture and the Formation of the Local Group", 1990 (ADS)

Peebles, P. J. E., "Tracing Galaxy Orbits Back in Time", 1989 (ADS)

## Theory for standard reconstruction

Coming soon

## Data papers with BAO fits

Coming soon

## Applications beyond BAO

Coming soon

## Forward modeling related

Under construction

While this is in the opposite direction of reconstruction of the initial condition, it is in many ways very similar.

Jamieson, D., et al., "Field-level Neural Network Emulator for Cosmological N-body Simulations", 2023 (ADS)

Field-level emulator for structure formation, two CNNs to output nonlinear displacement and velocity based on linear inputs, matter field

## Velocity reconstruction

Coming soon

A life-size bronze sculpture of Torosaurus in front of Yale Peabody Museum. This is a reconstruction (of Torosaurus).