Reconstructing the Large-Scale Velocity Field from DESI DR1 with Bayesian Inference

Raeed Mundow, Adi Nusser

Nov 3, 2026arXiv:2611.04830v1

astro-ph.CO

Scorecard· 16/16

5.0/10 impact

Competent, transparent first Bayesian velocity reconstruction on DESI DR1 BGS, but the validation and statistical power are limited and the results are largely preliminary or expected.

Abstract

Survey boundaries and nonlinear dynamics complicate reconstruction of large-scale matter-density and peculiar-velocity fields from galaxy redshift surveys. We develop and compare two reconstruction methods within a common Bayesian framework, based on linear perturbation theory and the Zel'dovich approximation, and apply them to the DESI Data Release 1 Bright Galaxy Survey. We infer the initial density field using a Gaussian prior and likelihood, with the Zel'dovich model displacing particles from a uniform Lagrangian grid. Both yield maximum a posteriori (MAP) fields; only the linear posterior is sampled. Our main findings are: \textit{(i)} Both reconstructions yield similar large-scale density structures and coherent velocity patterns in the survey interior, beyond roughly $50\,h^{-1}\,\mathrm{Mpc}$ from the footprint boundaries. \textit{(ii)} Comparison with Cosmicflows-4 groups, predominantly from the SDSS Fundamental Plane sample in the DESI overlap, shows close agreement between mean observed radial velocities and MAP predictions when binned by the latter, despite substantial individual scatter. \textit{(iii)} Both yield similar reflex-dipole profiles, defined as mean shell velocities relative to those at randomly sampled centres, out to $\sim225\,h^{-1}\,\mathrm{Mpc}$ . The profiles depend weakly on the prior normalization $σ_{8}$ , but lie below the fiducial linear $Λ$ CDM reference at $r<50\,h^{-1}\,\mathrm{Mpc}$ . Sparse sampling limits the largest radii. \textit{(iv)} In an exploratory BAO test, shifting galaxies and randoms to a target redshift $z = 8$ using reconstructed displacements sharpens the acoustic feature in both cases, with a slightly more pronounced peak for Zel'dovich. Survey geometry and galaxy bias remain the principal limitations.

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Impact assessment: Reconstructing the Large-Scale Velocity Field from DESI DR1 with Bayesian Inference

Core Contribution

The paper builds a common Bayesian forward-modelling framework for reconstructing the matter-density and peculiar-velocity fields from the DESI DR1 Bright Galaxy Survey (about 5.5M tracers, z≲0.5, a 3 h⁻¹Gpc box on a 256³ grid). Two dynamical models are implemented:

a linear model, solved as a Wiener filter by preconditioned conjugate gradients and sampled with Hoffman–Ribak constrained realizations;

a Zel'dovich particle-displacement model, with MAP found by L-BFGS using JAX automatic differentiation.

Both use a Gaussian prior on the initial field and a Gaussian likelihood on the redshift-space overdensity. The forward model includes light-cone evolution, a redshift-dependent bias, RSD and the survey mask. The authors then apply the reconstructions to:

a mock validation on MDPL2;

an independent comparison with Cosmicflows-4 group velocities;

a reflex-dipole profile out to about 225 h⁻¹Mpc;

an exploratory BAO reconstruction shifted to z=8.

The novelty is mostly in scale and application. Wiener-filter and Zel'dovich forward-model methods were already developed by Nusser and collaborators (2MRS, Lilow & Nusser 2021; Nusser 2026b). The step here is extending them to a DESI-volume, light-cone, survey-geometry setting that is roughly 10× larger, and doing a first DESI-based velocity-field reconstruction compared against CF4.

Methodological Rigor

Framework. The framework is coherent and the derivations are explicit: the redshift-space linear operator, the whitened parametrization, the normalized bias prescription that preserves positivity, and the TSC assignment chosen for differentiability. The numerical choices are sensible.

Validation. The MDPL2 tests are the weak point. They use a single z=0 snapshot, a different grid resolution (128³), halos with unit weights, and a uniform bias, and the configurations are idealized (a double-cone mask or a radial selection, never together). They do not include DESI light-cone mocks, so reconstruction errors on DESI are never calibrated. The authors state this openly.

Bias. The bias is a phenomenological ramp (b=1→2) that is fixed rather than inferred, so the linear-versus-Zel'dovich comparison is confounded with differing bias and assignment schemes. The authors note this.

CF4 test. The fitted slopes are 0.84±0.38 (linear) and 0.99±0.45 (Zel'dovich). They are consistent with unity but also with a wide range of other values. Individual scatter is about 5500 km/s, so the test has little discriminating power. There is no distance-error model and no treatment of Malmquist bias. As a test of gravitational instability or of Zel'dovich versus linear dynamics, it is weak.

Reflex dipole. Few independent spheres are available at large radius (N_c=11–23). The small-radius deficit relative to ΛCDM is flagged but not tested for significance.

BAO test. The BAO result is purely visual: no template fit, no covariance, and an unusual target of z=8. It cannot show improved accuracy or precision.

Uncertainty. The Zel'dovich posterior is not sampled. The linear posterior uses only 15 realizations. The diagonal noise covariance is an approximation.

Overall the design is careful and honest about its limits, but the evidence is largely qualitative or low-significance.

Potential Impact

The reconstructed fields could serve as a velocity and density prior or predictor for DESI Peculiar Velocity Survey analyses (FP and TF) and for kSZ velocity reconstruction. They could also feed luminosity-modulation tests and, potentially, BAO reconstruction. The authors say the fields are available on request, which limits community uptake.

Planned DR2 follow-ups, with DESI PV data, realistic mocks and growth-rate inference, would be the true tests. This paper is a stepping stone toward them rather than a result in its own right.

The Zel'dovich differentiable forward model in JAX is a reusable approach, but no code is released.

Timeliness & Relevance

The timing is good: DESI DR1 is public, DESI PV data is imminent, and kSZ and velocity-reconstruction work is growing. Interest in the growth rate and bulk-flow tension makes velocity-field reconstruction from redshift surveys relevant. The reflex-dipole deficit at r<50 h⁻¹Mpc is intriguing but not significant as presented. Competing reconstruction pipelines (BORG, pyrecon-type methods, Wiener filters) already exist, so the niche is specific.

Strengths

It is the first Bayesian velocity-field reconstruction on DESI BGS at this volume, with a transparent forward model.

The paper is unusually clear about caveats, and the appendices give derivations.

It uses an independent CF4 test with no leakage into the likelihood.

It develops both a linear model with sampled posterior and a nonlinear model with MAP, and compares them.

The conditional-mean convention (conditioning on the prediction, not the noisy observation) is correctly motivated.

Limitations

Calibration is missing: there are no DESI light-cone mocks, no error budget, and no end-to-end validation.

The fixed ad hoc bias is a key systematic.

The CF4 comparison has low statistical power (slope errors ~40–45%).

The BAO test is exploratory and has no quantitative metric.

The Zel'dovich model has no posterior sampling.

The reflex-dipole anomaly is not assessed for significance.

No cosmological parameters are inferred.

The preliminary framing and the requests-only data release reduce reusability.

The findings are mostly "consistent with ΛCDM / similar between methods", which is expected.

Other observations

It is a competent, incremental application paper in a niche subfield. Its main value is as a pipeline demonstration and baseline for later DESI PV analyses, not for its scientific conclusions. The results confirm expectations (the linear and Zel'dovich reconstructions agree in well-constrained interiors, and the slope matches unity within large errors) and so have low surprise. Compute is modest: a 256³ grid and a single GPU-class JAX workload are feasible for a small group, though DESI data access is needed.

Rating:5/ 10

Significance 4.5Rigor 5Novelty 4Clarity 7

Generated Nov 4, 2026

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Scorecard· 16/16

5.0/10 impact

Competent, transparent first Bayesian velocity reconstruction on DESI DR1 BGS, but the validation and statistical power are limited and the results are largely preliminary or expected.