arXiv subjects

Laurin Söding

Publications and source records attributed to Laurin Söding.

8 recordsLinked to original sources

arXiv2026

Variational Inference Using a Differentiable Multigrid Linear Solver

Gradient-based Bayesian inference methods require efficient access to Jacobian and adjoint-Jacobian operators of high-dimensional forward models. While multigrid solvers provide near-optimal complexity for elliptic partial differential equations, they are rarely available in forms compatible with automatic differentiation (AD). We develop a differentiable multigrid solver for steady-state diffusion-absorption problems and derive its adjoint operations analytically through the full multigrid hierarchy. The resulting solver, DMGS, is implemented in C++ and interfaced with JAX to provide efficient Jacobian-vector and vector-Jacobian products for variational inference in the NIFTy framework. We validate the approach on a 3D inverse problem involving diffuse radiative transfer in tissue, reconstructing an effective radiative source from Monte Carlo-simulated data. The reconstruction reproduces the data at a reduced chi-squared of 1.1 and generalizes to 32 independent validation datasets. Benchmarks against a JAX-native multigrid implementation show comparable runtimes and consistently lower peak memory for the hand-derived adjoint, with modest reverse-mode overhead. These results establish differentiable multigrid solvers as practical building blocks for variational inference in PDE-constrained problems.

math.NA↗

arXiv2026

Milky Way Atlas: A radial-velocity-resolved, three-dimensional map of H I within 1.25 kpc

We present a velocity-resolved three-dimensional map of local atomic hydrogen (HI) within 1.25 kpc of the Sun, tackling the challenge of converting emission from position-position-velocity space into true 3D structure. Our method combines the HI4PI full-sky survey with the Edenhofer et al. (2024) 3D dust map in the framework of Information Field Theory, enabling a joint reconstruction of the local HI density, radial velocity field, and effective line width while also separating emission arising inside the mapped local volume from more distant Galactic HI. The inference is driven by morphological matching between dust and HI structures together with kinematic coherence in 3D space. Synthetic data tests show that the method recovers the local density and velocity structure, even in the presence of substantial contamination from distant emission. The resulting map reveals a smoother, more diffuse local HI distribution than the dust, a declining HI-to-dust ratio toward high dust column densities consistent with the atomic-to-molecular transition, and a velocity field that captures both large-scale Galactic rotation and local non-circular velocities. Independent comparisons with maser and young stellar cluster velocities agree with the recovered kinematics. This HI map provides a new three-dimensional, kinematically resolved view of the nearby atomic interstellar medium and a foundation for localising other velocity-resolved Galactic emission in physical space.

astro-ph.GA↗

arXiv2026

A Three-Dimensional Tomographic Reconstruction of the Galactic Cosmic-Ray Proton Density

Cosmic rays (CRs) are a ubiquitous non-thermal component of the interstellar medium (ISM). A data-driven three-dimensional (3D) map of their distribution is essential for understanding CR transport and constraining the spatial distribution of their sources. In this work, we reconstructed the 3D spatial distribution of the Galactic cosmic-ray proton (CRp) density. We model the diffuse gamma-ray emission arising from inelastic hadronic interactions between CRps and interstellar gas. Using a map of dust-correlated diffuse gamma-ray emission based on ten years of Fermi-LAT observations together with a three-dimensional gas density model, we infer the spatial CRp distribution through a morphological matching approach. The logarithmic CRp density field is described by a Gaussian process defined on a spherical-times-radial grid, while both the field and its correlation structure are inferred simultaneously using Iterative Charted Refinement. The posterior distribution of the reconstructed 3D CRp density field is approximated using geometric variational inference. The reconstructed CRp density exhibits a smooth but spatially structured distribution with a limited dynamical range across the Galactic disk. We find a moderate enhancement of the CRp density toward the inner Galaxy. The inferred normalization at the Solar position is consistent with local CR measurements by the AMS-02 instrument.

astro-ph.HE↗

arXiv2025

Spatially Coherent 3D Distributions of HI and CO in the Milky Way

The spatial distribution of the gaseous components of the Milky Way is of great importance for a number of different fields, for example, Galactic structure, star formation, and cosmic rays. However, obtaining distance information to gaseous clouds in the interstellar medium from Doppler-shifted line emission is notoriously difficult given our vantage point in the Galaxy. It requires spatial knowledge of gas velocities and generally suffers from distance ambiguities. Previous works often assumed the optically thin limit, had a fixed velocity field, and lacked resolution overall. We aim to overcome these issues and improve previous reconstructions of the gaseous constituents of the interstellar medium of the Galaxy. We used 3D Gaussian processes to model correlations in the interstellar medium, including correlations between different lines of sight, and enforce a spatially coherent structure in the prior. For modelling the transport of radiation from the emitting gas to us as observers, we took absorption effects into account. A special numerical grid ensures that there is high resolution nearby. We inferred the spatial distributions of atomic hydrogen (HI), carbon monoxide (CO), their emission line widths, and the Galactic velocity field in a joint Bayesian inference. We further constrained these fields with complementary data from Galactic masers and young stellar object clusters. Our main result consists of a set of samples that implicitly contain statistical uncertainties. The resulting maps are spatially coherent and reproduce the data with high fidelity. We confirm previous findings regarding the warping and flaring of the Galactic disc. A comparison with 3D dust maps reveals a good agreement on scales larger than approximately 400 pc. While our results are not free of artefacts, they present a big step forward in obtaining high-quality 3D maps of the interstellar medium.

astro-ph.GA↗

arXiv2025

Local dark matter density from Gaia DR3 K-dwarfs using Gaussian processes

The local dark matter density provides constraints on dark matter models and is of importance for experiments hoping to detect dark matter particles in the laboratory. The advent of extensive survey data calls for more complex physical modelling and more sophisticated statistical analysis, particularly to account for correlated uncertainties. In this paper, we perform a vertical Jeans analysis, including a local approximation of the tilt term, using a sample of $200\,000$ K-dwarf stars from the Gaia DR3 catalogue. After combination with the Survey-of-Surveys (SoS) catalogue, $160\,888$ of those have radial velocity measurements. We use Gaussian processes as priors for the covariance matrix of radial and vertical velocities. Joint inference of the posterior distribution of the local dark matter density and the velocity moments is performed using geometric variational inference. We find a local dark matter density of ${ρ_\mathrm{dm} = 0.0117 \pm 0.0035\, \mathrm{M}_\odot\,\mathrm{pc}^{-3} = 0.44 \pm 0.13\, \mathrm{GeV}\,\mathrm{cm}^{-3}}$ at the Sun's position, which is in agreement with most other recent analyses. By comparing a ($z$-dependent) Gaussian process prior with a ($z$-independent) scalar prior for the tilt term, we quantify its impact on estimates of the local dark matter density and argue that careful modelling is required to mitigate systematic biases.

astro-ph.GA↗

arXiv2025

The influence of the 3D Galactic gas structure on cosmic-ray transport and $γ$-ray emission

Cosmic rays (CRs) play a major role in the dynamics of the interstellar medium (ISM). Their interactions and transport ionize, heat, and push the ISM thereby coupling different regions of it. The spatial distribution of CRs depends on the distribution of their sources as well as the ISM constituents they interact with, such as gas, starlight, and magnetic fields. Particularly, gas influences CR fluxes and $γ$-ray emission. We illustrate the influence of realistic and largely structured 3D gas distributions on CR transport and $γ$-ray emission, by studying their correlation using the PICARD code and multiple samples of recent 3D reconstructions of the HI and H2 Galactic gas constituents. We adjust the diffusion coefficient $D_{xx}$ and Alfvén speed $v_{\text{A}}$ to reproduce local measurements of B/C abundances and find that these parameters depend non-linearly on the local distribution of gas. When simulating CR transport, the distributions of CR fluxes exhibit energy-dependent structures that vary for all CR species due to their corresponding loss processes. Regions of enhanced secondary (primary) species are spatially correlated (anti-correlated) with the gas density. Furthermore, we show that the morphology of gas clouds alone impacts CR flux predictions. For $γ$-ray emission, we observe a high sensitivity of the $γ$-ray emissivities to gas structures, as these determine the spatial distributions of hadronic interactions and bremsstrahlung. This way, we have for the first time calculated how well-defined uncertainties in a structured gas model propagate to CR transport and $γ$-ray emission.

astro-ph.HE↗

arXiv2023

Bayesian inference of 3D densities of galactic HI and H2

Due to our vantage point in the disk of the Galaxy, its 3D structure is not directly accessible. However, knowing the spatial distribution, e.g. of atomic and molecular hydrogen gas is of great importance for interpreting and modelling cosmic ray data and diffuse emission. Using novel Bayesian inference techniques, we reconstruct the 3D densities of atomic and molecular hydrogen in the Galaxy together with (part of) the galactic velocity field. In order to regularise the infinite number of degrees of freedom and obtain information in regions with missing or insufficient data, we incorporate the correlation structure of the gas fields into our prior. Basis for these reconstructions are the data-sets from the HI4PI-survey on the 21-cm emission line and the CO-survey compilation by Dame et al. (2001) on the ($1\rightarrow0$) rotational transition together with a variable gas flow model. We present the preliminary estimated mean surface mass densities and corrections to the prior assumption of the galactic velocity field. In the future, we plan to relax assumptions on the optical thickness and include additional data to further constrain either the galactic velocity field or the gas densities.

astro-ph.GA↗

arXiv2020

Evolving Ultralight Scalars into Non-Linearity with Lagrangian Perturbation Theory

Many models of high energy physics suggest that the cosmological dark sector consists of not just one, but a spectrum of ultralight scalar particles with logarithmically distributed masses. To study the potential signatures of low concentrations of ultralight axion (also known as fuzzy) dark matter, we modify Lagrangian perturbation theory (LPT) by distinguishing between trajectories of different dark matter species. We further adapt LPT to include the effects of a quantum pressure, which is necessary to generate correct initial conditions for ultralight axion simulations. Based on LPT, our modified scheme is extremely efficient on large scales and it can be extended to an arbitrary number of particle species at very little computational cost. This allows for computation of self-consistent initial conditions in mixed dark matter models. Additionally, we find that shell-crossing is delayed for ultralight particles and that the deformation tensor extracted from LPT can be used to identify the range of redshifts and scales for which the Madelung formalism of fuzzy dark matter is a reliable approximation.

astro-ph.CO↗