{% raw %} Title: Create a Markdown Blog Post Integrating Research Details and a Featured Paper ==================================================================================== This task involves generating a Markdown file (ready for a GitHub-served Jekyll site) that integrates our research details with a featured research paper. The output must follow the exact format and conventions described below. ==================================================================================== Output Format (Markdown): ------------------------------------------------------------------------------------ --- layout: post title: "Predicting the Subhalo Mass Functions in Simulations from Galaxy Images" date: 2025-10-16 categories: papers --- ![AI generated image](/assets/images/posts/2025-10-16-2510.14766.png) Chris Lovell Content generated by [gemini-2.5-pro](https://deepmind.google/technologies/gemini/) using [this prompt](/prompts/content/2025-10-16-2510.14766.txt). Image generated by [imagen-4.0-generate-001](https://deepmind.google/technologies/gemini/) using [this prompt](/prompts/images/2025-10-16-2510.14766.txt). ------------------------------------------------------------------------------------ ==================================================================================== Please adhere strictly to the following instructions: ==================================================================================== Section 1: Content Creation Instructions ==================================================================================== 1. **Generate the Page Body:** - Write a well-composed, engaging narrative that is suitable for a scholarly audience interested in advanced AI and astrophysics. - Ensure the narrative is original and reflective of the tone and style and content in the "Homepage Content" block (provided below), but do not reuse its content. - Use bullet points, subheadings, or other formatting to enhance readability. 2. **Highlight Key Research Details:** - Emphasize the contributions and impact of the paper, focusing on its methodology, significance, and context within current research. - Specifically highlight the lead author ({'name': 'Andreas Filipp'}). When referencing any author, use Markdown links from the Author Information block (choose academic or GitHub links over social media). 3. **Integrate Data from Multiple Sources:** - Seamlessly weave information from the following: - **Paper Metadata (YAML):** Essential details including the title and authors. - **Paper Source (TeX):** Technical content from the paper. - **Bibliographic Information (bbl):** Extract bibliographic references. - **Author Information (YAML):** Profile details for constructing Markdown links. - Merge insights from the Paper Metadata, TeX source, Bibliographic Information, and Author Information blocks into a coherent narrative—do not treat these as separate or isolated pieces. - Insert the generated narrative between the HTML comments: and 4. **Generate Bibliographic References:** - Review the Bibliographic Information block carefully. - For each reference that includes a DOI or arXiv identifier: - For DOIs, generate a link formatted as: [10.1234/xyz](https://doi.org/10.1234/xyz) - For arXiv entries, generate a link formatted as: [2103.12345](https://arxiv.org/abs/2103.12345) - **Important:** Do not use any LaTeX citation commands (e.g., `\cite{...}`). Every reference must be rendered directly as a Markdown link. For example, instead of `\cite{mycitation}`, output `[mycitation](https://doi.org/mycitation)` - **Incorrect:** `\cite{10.1234/xyz}` - **Correct:** `[10.1234/xyz](https://doi.org/10.1234/xyz)` - Ensure that at least three (3) of the most relevant references are naturally integrated into the narrative. - Ensure that the link to the Featured paper [2510.14766](https://arxiv.org/abs/2510.14766) is included in the first sentence. 5. **Final Formatting Requirements:** - The output must be plain Markdown; do not wrap it in Markdown code fences. - Preserve the YAML front matter exactly as provided. ==================================================================================== Section 2: Provided Data for Integration ==================================================================================== 1. **Homepage Content (Tone and Style Reference):** ```markdown --- layout: home --- ![AI generated image](/assets/images/index.png) The Handley Research Group stands at the forefront of cosmological exploration, pioneering novel approaches that fuse fundamental physics with the transformative power of artificial intelligence. We are a dynamic team of researchers, including PhD students, postdoctoral fellows, and project students, based at the University of Cambridge. Our mission is to unravel the mysteries of the Universe, from its earliest moments to its present-day structure and ultimate fate. We tackle fundamental questions in cosmology and astrophysics, with a particular focus on leveraging advanced Bayesian statistical methods and AI to push the frontiers of scientific discovery. Our research spans a wide array of topics, including the [primordial Universe](https://arxiv.org/abs/1907.08524), [inflation](https://arxiv.org/abs/1807.06211), the nature of [dark energy](https://arxiv.org/abs/2503.08658) and [dark matter](https://arxiv.org/abs/2405.17548), [21-cm cosmology](https://arxiv.org/abs/2210.07409), the [Cosmic Microwave Background (CMB)](https://arxiv.org/abs/1807.06209), and [gravitational wave astrophysics](https://arxiv.org/abs/2411.17663). ### Our Research Approach: Innovation at the Intersection of Physics and AI At The Handley Research Group, we develop and apply cutting-edge computational techniques to analyze complex astronomical datasets. Our work is characterized by a deep commitment to principled [Bayesian inference](https://arxiv.org/abs/2205.15570) and the innovative application of [artificial intelligence (AI) and machine learning (ML)](https://arxiv.org/abs/2504.10230). **Key Research Themes:** * **Cosmology:** We investigate the early Universe, including [quantum initial conditions for inflation](https://arxiv.org/abs/2002.07042) and the generation of [primordial power spectra](https://arxiv.org/abs/2112.07547). We explore the enigmatic nature of [dark energy, using methods like non-parametric reconstructions](https://arxiv.org/abs/2503.08658), and search for new insights into [dark matter](https://arxiv.org/abs/2405.17548). A significant portion of our efforts is dedicated to [21-cm cosmology](https://arxiv.org/abs/2104.04336), aiming to detect faint signals from the Cosmic Dawn and the Epoch of Reionization. * **Gravitational Wave Astrophysics:** We develop methods for [analyzing gravitational wave signals](https://arxiv.org/abs/2411.17663), extracting information about extreme astrophysical events and fundamental physics. * **Bayesian Methods & AI for Physical Sciences:** A core component of our research is the development of novel statistical and AI-driven methodologies. This includes advancing [nested sampling techniques](https://arxiv.org/abs/1506.00171) (e.g., [PolyChord](https://arxiv.org/abs/1506.00171), [dynamic nested sampling](https://arxiv.org/abs/1704.03459), and [accelerated nested sampling with $\beta$-flows](https://arxiv.org/abs/2411.17663)), creating powerful [simulation-based inference (SBI) frameworks](https://arxiv.org/abs/2504.10230), and employing [machine learning for tasks such as radiometer calibration](https://arxiv.org/abs/2504.16791), [cosmological emulation](https://arxiv.org/abs/2503.13263), and [mitigating radio frequency interference](https://arxiv.org/abs/2211.15448). We also explore the potential of [foundation models for scientific discovery](https://arxiv.org/abs/2401.00096). **Technical Contributions:** Our group has a strong track record of developing widely-used scientific software. Notable examples include: * [**PolyChord**](https://arxiv.org/abs/1506.00171): A next-generation nested sampling algorithm for Bayesian computation. * [**anesthetic**](https://arxiv.org/abs/1905.04768): A Python package for processing and visualizing nested sampling runs. * [**GLOBALEMU**](https://arxiv.org/abs/2104.04336): An emulator for the sky-averaged 21-cm signal. * [**maxsmooth**](https://arxiv.org/abs/2007.14970): A tool for rapid maximally smooth function fitting. * [**margarine**](https://arxiv.org/abs/2205.12841): For marginal Bayesian statistics using normalizing flows and KDEs. * [**fgivenx**](https://arxiv.org/abs/1908.01711): A package for functional posterior plotting. * [**nestcheck**](https://arxiv.org/abs/1804.06406): Diagnostic tests for nested sampling calculations. ### Impact and Discoveries Our research has led to significant advancements in cosmological data analysis and yielded new insights into the Universe. Key achievements include: * Pioneering the development and application of advanced Bayesian inference tools, such as [PolyChord](https://arxiv.org/abs/1506.00171), which has become a cornerstone for cosmological parameter estimation and model comparison globally. * Making significant contributions to the analysis of major cosmological datasets, including the [Planck mission](https://arxiv.org/abs/1807.06209), providing some of the tightest constraints on cosmological parameters and models of [inflation](https://arxiv.org/abs/1807.06211). * Developing novel AI-driven approaches for astrophysical challenges, such as using [machine learning for radiometer calibration in 21-cm experiments](https://arxiv.org/abs/2504.16791) and [simulation-based inference for extracting cosmological information from galaxy clusters](https://arxiv.org/abs/2504.10230). * Probing the nature of dark energy through innovative [non-parametric reconstructions of its equation of state](https://arxiv.org/abs/2503.08658) from combined datasets. * Advancing our understanding of the early Universe through detailed studies of [21-cm signals from the Cosmic Dawn and Epoch of Reionization](https://arxiv.org/abs/2301.03298), including the development of sophisticated foreground modelling techniques and emulators like [GLOBALEMU](https://arxiv.org/abs/2104.04336). * Developing new statistical methods for quantifying tensions between cosmological datasets ([Quantifying tensions in cosmological parameters: Interpreting the DES evidence ratio](https://arxiv.org/abs/1902.04029)) and for robust Bayesian model selection ([Bayesian model selection without evidences: application to the dark energy equation-of-state](https://arxiv.org/abs/1506.09024)). * Exploring fundamental physics questions such as potential [parity violation in the Large-Scale Structure using machine learning](https://arxiv.org/abs/2410.16030). ### Charting the Future: AI-Powered Cosmological Discovery The Handley Research Group is poised to lead a new era of cosmological analysis, driven by the explosive growth in data from next-generation observatories and transformative advances in artificial intelligence. Our future ambitions are centred on harnessing these capabilities to address the most pressing questions in fundamental physics. **Strategic Research Pillars:** * **Next-Generation Simulation-Based Inference (SBI):** We are developing advanced SBI frameworks to move beyond traditional likelihood-based analyses. This involves creating sophisticated codes for simulating [Cosmic Microwave Background (CMB)](https://arxiv.org/abs/1908.00906) and [Baryon Acoustic Oscillation (BAO)](https://arxiv.org/abs/1607.00270) datasets from surveys like DESI and 4MOST, incorporating realistic astrophysical effects and systematic uncertainties. Our AI initiatives in this area focus on developing and implementing cutting-edge SBI algorithms, particularly [neural ratio estimation (NRE) methods](https://arxiv.org/abs/2407.15478), to enable robust and scalable inference from these complex simulations. * **Probing Fundamental Physics:** Our enhanced analytical toolkit will be deployed to test the standard cosmological model ($\Lambda$CDM) with unprecedented precision and to explore [extensions to Einstein's General Relativity](https://arxiv.org/abs/2006.03581). We aim to constrain a wide range of theoretical models, from modified gravity to the nature of [dark matter](https://arxiv.org/abs/2106.02056) and [dark energy](https://arxiv.org/abs/1701.08165). This includes leveraging data from upcoming [gravitational wave observatories](https://arxiv.org/abs/1803.10210) like LISA, alongside CMB and large-scale structure surveys from facilities such as Euclid and JWST. * **Synergies with Particle Physics:** We will continue to strengthen the connection between cosmology and particle physics by expanding the [GAMBIT framework](https://arxiv.org/abs/2009.03286) to interface with our new SBI tools. This will facilitate joint analyses of cosmological and particle physics data, providing a holistic approach to understanding the Universe's fundamental constituents. * **AI-Driven Theoretical Exploration:** We are pioneering the use of AI, including [large language models and symbolic computation](https://arxiv.org/abs/2401.00096), to automate and accelerate the process of theoretical model building and testing. This innovative approach will allow us to explore a broader landscape of physical theories and derive new constraints from diverse astrophysical datasets, such as those from GAIA. Our overarching goal is to remain at the forefront of scientific discovery by integrating the latest AI advancements into every stage of our research, from theoretical modeling to data analysis and interpretation. We are excited by the prospect of using these powerful new tools to unlock the secrets of the cosmos. Content generated by [gemini-2.5-pro-preview-05-06](https://deepmind.google/technologies/gemini/) using [this prompt](/prompts/content/index.txt). Image generated by [imagen-3.0-generate-002](https://deepmind.google/technologies/gemini/) using [this prompt](/prompts/images/index.txt). ``` 2. **Paper Metadata:** ```yaml !!python/object/new:feedparser.util.FeedParserDict dictitems: id: http://arxiv.org/abs/2510.14766v1 guidislink: true link: https://arxiv.org/abs/2510.14766v1 title: Predicting the Subhalo Mass Functions in Simulations from Galaxy Images title_detail: !!python/object/new:feedparser.util.FeedParserDict dictitems: type: text/plain language: null base: '' value: Predicting the Subhalo Mass Functions in Simulations from Galaxy Images updated: '2025-10-16T15:02:42Z' updated_parsed: !!python/object/apply:time.struct_time - !!python/tuple - 2025 - 10 - 16 - 15 - 2 - 42 - 3 - 289 - 0 - tm_zone: null tm_gmtoff: null links: - !!python/object/new:feedparser.util.FeedParserDict dictitems: href: https://arxiv.org/abs/2510.14766v1 rel: alternate type: text/html - !!python/object/new:feedparser.util.FeedParserDict dictitems: href: https://arxiv.org/pdf/2510.14766v1 rel: related type: application/pdf title: pdf summary: Strong gravitational lensing provides a powerful tool to directly infer the dark matter (DM) subhalo mass function (SHMF) in lens galaxies. However, comparing observationally inferred SHMFs to theoretical predictions remains challenging, as the predicted SHMF can vary significantly between galaxies - even within the same cosmological model - due to differences in the properties and environment of individual galaxies. We present a machine learning framework to infer the galaxy-specific predicted SHMF from galaxy images, conditioned on the assumed inverse warm DM particle mass $M^{-1}_{\rm DM}$. To train the model, we use 1024 high-resolution hydrodynamical zoom-in simulations from the DREAMS suite. Mock observations are generated using Synthesizer, excluding gas particle contributions, and SHMFs are computed with the Rockstar halo finder. Our neural network takes as input both the galaxy images and the inverse DM mass. This method enables scalable, image-based predictions for the theoretical DM SHMFs of individual galaxies, facilitating direct comparisons with observational measurements. summary_detail: !!python/object/new:feedparser.util.FeedParserDict dictitems: type: text/plain language: null base: '' value: Strong gravitational lensing provides a powerful tool to directly infer the dark matter (DM) subhalo mass function (SHMF) in lens galaxies. However, comparing observationally inferred SHMFs to theoretical predictions remains challenging, as the predicted SHMF can vary significantly between galaxies - even within the same cosmological model - due to differences in the properties and environment of individual galaxies. We present a machine learning framework to infer the galaxy-specific predicted SHMF from galaxy images, conditioned on the assumed inverse warm DM particle mass $M^{-1}_{\rm DM}$. To train the model, we use 1024 high-resolution hydrodynamical zoom-in simulations from the DREAMS suite. Mock observations are generated using Synthesizer, excluding gas particle contributions, and SHMFs are computed with the Rockstar halo finder. Our neural network takes as input both the galaxy images and the inverse DM mass. This method enables scalable, image-based predictions for the theoretical DM SHMFs of individual galaxies, facilitating direct comparisons with observational measurements. tags: - !!python/object/new:feedparser.util.FeedParserDict dictitems: term: astro-ph.CO scheme: http://arxiv.org/schemas/atom label: null - !!python/object/new:feedparser.util.FeedParserDict dictitems: term: astro-ph.GA scheme: http://arxiv.org/schemas/atom label: null published: '2025-10-16T15:02:42Z' published_parsed: !!python/object/apply:time.struct_time - !!python/tuple - 2025 - 10 - 16 - 15 - 2 - 42 - 3 - 289 - 0 - tm_zone: null tm_gmtoff: null arxiv_comment: Published as a workshop paper at the ML4Astro Workshop at ICML 2025 arxiv_primary_category: term: astro-ph.CO authors: - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: Andreas Filipp - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: Tri Nguyen - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: Laurence Perreault-Levasseur - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: Jonah Rose - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: Chris Lovell - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: Nicolas Payot - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: Francisco Villaescusa-Navarro - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: Yashar Hezaveh author_detail: !!python/object/new:feedparser.util.FeedParserDict dictitems: name: Yashar Hezaveh author: Yashar Hezaveh ``` 3. **Paper Source (TeX):** ```tex %%%%%%%% ICML 2025 EXAMPLE LATEX SUBMISSION FILE %%%%%%%%%%%%%%%%% \documentclass{article} \usepackage{microtype} \usepackage{graphicx} \usepackage{subfigure} \usepackage{booktabs} % for professional tables \usepackage{hyperref} % Attempt to make hyperref and algorithmic work together better: \newcommand{\theHalgorithm}{\arabic{algorithm}} \usepackage[accepted]{ml4astro2025} % For theorems and such \usepackage{amsmath} \usepackage{amssymb} \usepackage{mathtools} \usepackage{amsthm} \usepackage{soul} % if you use cleveref.. \usepackage[capitalize,noabbrev]{cleveref} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % THEOREMS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \theoremstyle{plain} \newtheorem{theorem}{Theorem}[section] \newtheorem{proposition}[theorem]{Proposition} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{assumption}[theorem]{Assumption} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} % Todonotes is useful during development; simply uncomment the next line % and comment out the line below the next line to turn off comments %\usepackage[disable,textsize=tiny]{todonotes} \usepackage[textsize=tiny]{todonotes} %%%% Compatibility with ml4astro2025.sty commands \newcommand{\icmltitle}{\mlforastrotitle} \newcommand{\icmltitlerunning}{\mlforastrotitlerunning} \newcommand{\icmlauthor}{\mlforastroauthor} \newcommand{\icmlaffiliation}{\mlforastroaffiliation} \newcommand{\icmlcorrespondingauthor}{\mlforastrocorrespondingauthor} \newcommand{\icmlkeywords}{\mlforastrokeywords} \newcommand{\icmlEqualContribution}{\mlforastroEqualContribution} \newcommand{\icmlsetsymbol}{\mlforastrosetsymbol} \newenvironment{icmlauthorlist} {\begin{mlforastroauthorlist}} {\end{mlforastroauthorlist}} \newcommand{\tn}[1]{{(\color{red}TN: #1)}} \icmltitlerunning{Predicting the Subhalo Mass Functions in Simulations from Galaxy Images} \begin{document} \twocolumn[ \icmltitle{Predicting the Subhalo Mass Functions in Simulations from Galaxy Images} \icmlsetsymbol{equal}{*} \begin{icmlauthorlist} \icmlauthor{Andreas Filipp}{UdeM,MILA,CIELA} \icmlauthor{Tri Nguyen}{CIERA,SKAI} \icmlauthor{Laurence Perreault-Levasseur}{UdeM,MILA,CIELA,Flatiron,Perimeter,TSI} \icmlauthor{Jonah Rose}{CCA} \icmlauthor{Chris Lovell}{Kavli,InstituteOfAstro} \icmlauthor{Nicolas Payot}{UdeM,MILA,CIELA} \icmlauthor{Francisco Villaescusa-Navarro}{Princeton,Simons} \icmlauthor{Yashar Hezaveh}{UdeM,MILA,CIELA,Flatiron,TSI} \end{icmlauthorlist} \icmlaffiliation{UdeM}{Department of Physics, University of Montreal, Montreal, Canada} \icmlaffiliation{MILA}{MILA Quebec AI Institute, Montreal, Canada} \icmlaffiliation{CIELA}{CIELA Institute, Montreal Institute for Astrophysics and Machine Learning, Montreal, Canada} \icmlaffiliation{Flatiron}{Center for Computational Astrophysics, Flatiron Institute, New York, USA} \icmlaffiliation{Perimeter}{Perimeter Institute for Theoretical Physics, Waterloo, Canada} \icmlaffiliation{TSI}{Trottier Space Institute, McGill University, Montreal, Canada} \icmlaffiliation{CIERA}{Center for Interdisciplinary Exploration and Research in Astrophysics, Northwestern University, Evanston, USA} \icmlaffiliation{SKAI}{The NSF-Simons AI Institute for the Sky, Chicago, USA} \icmlaffiliation{CCA}{Center for Computational Astrophysics, New York, USA} \icmlaffiliation{Princeton}{Princeton University, Princeton, USA} \icmlaffiliation{Simons}{Simons Foundation, New York, USA} % \icmlaffiliation{Portsmouth}{University of Portsmouth, Portsmouth, UK} \icmlaffiliation{Kavli}{Kavli Institute for Cosmology, Madingley Road, Cambridge, UK} \icmlaffiliation{InstituteOfAstro}{Institute of Astronomy, Madingley Road, Cambridge, UK} \icmlcorrespondingauthor{Andreas Filipp}{andreas.filipp@umontreal.ca} \icmlkeywords{Machine Learning, ICML, Astrophysics, Dark Matter} \vskip 0.3in ] \printAffiliationsAndNotice{} \begin{abstract} Strong gravitational lensing provides a powerful tool to directly infer the dark matter (DM) subhalo mass function (SHMF) in lens galaxies. However, comparing observationally inferred SHMFs to theoretical predictions remains challenging, as the predicted SHMF can vary significantly between galaxies — even within the same cosmological model — due to differences in the properties and environment of individual galaxies. We present a machine learning framework to infer the galaxy-specific predicted SHMF from galaxy images, conditioned on the assumed inverse warm DM particle mass $M^{-1}_{\rm DM}$. To train the model, we use 1024 high-resolution hydrodynamical zoom-in simulations from the DREAMS suite. Mock observations are generated using \texttt{Synthesizer}, excluding gas particle contributions, and SHMFs are computed with the \texttt{Rockstar} halo finder. Our neural network takes as input both the galaxy images and the inverse DM mass. This method enables scalable, image-based predictions for the theoretical DM SHMFs of individual galaxies, facilitating direct comparisons with observational measurements. \end{abstract} \vspace{-10mm} \section{Introduction} One of the most striking open questions in modern astrophysics is the nature of dark matter (DM), which constitutes approximately 80\% of the universe’s matter content \citep[e.g.,][]{WMAP_2013, Planck_2020}. While its presence is inferred from gravitational phenomena across a wide range of cosmic scales, from galaxy clusters to large-scale structure, DM has yet to be detected through any non-gravitational interactions, and its fundamental properties remain unknown. Different models predict distinct clustering behaviors for DM, especially on small, sub-galactic scales. On these scales, the distribution of dark matter — quantified by the subhalo mass function (SHMF) — is highly sensitive to its particle nature, making it a powerful discriminator between DM models \citep[e.g.,][]{Ferreira_2021_DM}. In warm DM (WDM) scenarios, for example, smaller particle masses correspond to higher thermal velocities, which suppress the formation of low-mass halos below the free-streaming scale \citep[e.g.,][]{Colin_2000_WDM, Gilman_2020_HMF, Loudas_2022_WDM}. Strong gravitational lensing provides a unique way to probe the distribution of matter on these small scales. Unlike methods that rely on luminous tracers, lensing is sensitive to all matter — luminous or dark — making it a powerful observational tool to constrain the SHMF. Traditional analyses infer the presence of individual subhalos by evaluating whether introducing localized perturbers to a smooth lens model leads to a statistically significant improvement in the fit to the observed lensed images \citep[e.g.,][]{Vegetti_2010, Yashar_2016}. More recently, simulation-based studies have demonstrated that machine learning approaches could enable population-level inference of the SHMF by combining data across ensembles of lensing systems \citep[e.g.,][]{brehmer2019mining, Brehmer_Sidd_2019_NRE, Coogan_2022, Zhang_2022, Wagner_C2023, Wagner_C2024, Zhang_2024, OOD_paper_24}. However, connecting these observational constraints to theoretical predictions remains challenging. Even within a fixed cosmology, the SHMF depends on properties of individual galaxies, including, for example, total mass, morphology, merger history, and local environment \citep[e.g.,][]{Yashar_2016_powerspec}, leading to significant system-to-system variation. In this work, we introduce a machine learning framework to predict theoretical SHMFs directly from galaxy images, conditioned on an assumed WDM mass. Its goal is to predict, given a WDM particle mass, a plausible theoretical range of SHMFs for specific individual galaxies based on their observable properties. These predictions can then be tested against observational constraints, such as those coming from galaxy-galaxy strong gravitational lensing, to place limits on the WDM mass. To make these predictions, we use the DREAMS simulation suite~\citep{{Jonah_DREAMS_2025}}, as well as \texttt{Synthesizer}~\citep{Vijayan_2020_synthesizer} to create realistic galaxy images. Our method accounts for inter-galaxy variability and enables scalable, image-based inference of theoretical predictions. This approach provides a new pathway to compare dark matter models with forthcoming lensing observations, enabling more precise, per-galaxy tests of DM’s small-scale gravitational effects. The paper is structured as follows: In Section~\ref{sec:DREAMS}, we describe the hydrodynamical simulation suite used in this work. Section~\ref{sec:Methods} begins with an overview of how we created the galaxy images from the hydrodynamical simulations, then provides the assumed SHMF profile and the correlation with different DM models, as well as the neural network architecture used to make predictions. Section~\ref{sec:Results} presents our results, and we conclude in Section~\ref{sec:Discussion}. \section{DREAMS Simulations} \label{sec:DREAMS} The DREAMS simulation suite contains, among other products, a set of high-resolution cosmological zoom-in hydrodynamic simulations designed to explore galaxy formation under varying DM and baryonic physics. Each zoom-in simulation is run using the \texttt{AREPO} code \cite{Springel_2010_AREPO, Springel_2019_AREPO, Weinberger_2020_AREPO}, enabling accurate modeling of complex baryonic processes such as gas cooling, star formation, and feedback. The initial conditions for each zoom-in are constructed by selecting a random, isolated Milky Way–mass halo from a low-resolution volume, then iteratively refining its Lagrangian region using intermediate- and high-resolution particle resampling to define the zoom-in domain \citep[see][]{Jonah_DREAMS_2025}. These zoom-in simulations are performed across a range of different WDM models in the range $M_{\rm DM} \in [1.8, 30.3]\, \mathrm{keV}$, sampled uniformly in the inverse $M^{-1}_{\rm DM}$. Further, the supernova (SN) wind, SN energy, and active galactic nuclei (AGN) parameters vary between each zoom-in simulation \cite{Jonah_DREAMS_2025}. The simulations are modeled using the IllustrisTNG baryonic physics prescriptions. By varying both the DM physics and feedback parameters, the DREAMS simulations allow us to marginalize over baryonic uncertainties and learn a mapping from observable galaxy properties and WDM masses to the underlying SHMF. This marginalization ensures that our model generalizes across different astrophysical scenarios. The DM sub-halos in the WDM zoom-in simulations are identified using the \texttt{Rockstar} halo finder \cite{Behroozi_2013_Rockstar}. At the time of submitting this work, \texttt{Rockstar} halo catalogs were made available for 815 of the 1024 DREAMS zoom-in simulations. These constitute the labeled dataset used for supervised training of the SHMF inference model. \section{Methods} \label{sec:Methods} \begin{figure} \centering \includegraphics[width=1.\linewidth]{Images/Flowchart_train_label.png} \vspace{-8.5mm} \caption{\textbf{A flowchart showing the training procedure, label generation, and inference.}} \label{fig:flow_architecture} \vspace{-5.5mm} \end{figure} \subsection{Image Generation with Synthesizer} \label{sec:Synthesizer} Creating realistic galaxy images from hydrodynamic simulations typically requires computationally expensive radiative transfer simulations. As an efficient alternative, we use \texttt{Synthesizer} \cite{Wilkins_2020_synthesizer, Vijayan_2020_synthesizer} to generate realistic observational mock images from simulated galaxies. For each of the 815 zoom-in galaxies with available \texttt{Rockstar}-catalog, we generate 12 different projections by varying the line-of-sight orientation of the particles. \texttt{Synthesizer} produces galaxy images by generating spatially resolved spectral energy distributions (SEDs) and applying instrument-specific wavelength filters from the Spanish Virtual Observatory (SVO) filter service\footnote{\url{https://svo2.cab.inta-csic.es/theory/fps/}} \cite{Rodrigo_2012_SVO, Rodrigo_2020_SVO, Rodrigo_2024_SVO}. A detailed description of the image creation process can be found in Appendix~\ref{app:synthesizer}. Examples of the generated galaxy images are shown in Figure~\ref{fig:NF_visual_comp}, alongside their corresponding galaxy-specific SHMFs. \subsection{Dark Matter Subhalo Mass Function} Since we aim to learn a mapping between galaxy images and their corresponding SHMF for a given WDM mass, we next move on to modeling the functional form of galaxies' SHMFs. We assume this functional form of the DM SHMFs to be a power-law with a slope of $-0.9$, as an approximation to theoretical predictions of cold DM (CDM) \citep[e.g.,][]{Kuhlen_2007_ViaLactea, Diemand_2007_ViaLactea, Springel_2008, Hiroshima_2018}. To model the subhalo mass function of WDM, we add to the power-law form of CDM a low-mass cutoff \citep[e.g.,][]{Gilman_2020_HMF}: \begin{equation} \begin{split} \frac{dN}{dm}|_{\rm wdm} &= \frac{dN}{dm}|_{\rm CDM} \cdot \left( 1+ \left( \frac{m_{\rm wdm}}{m} \right) \right)^{-1.3} \\ &= A \cdot m^{-0.9} \cdot \left( 1+ \left( \frac{m_{\rm wdm}}{m} \right) \right)^{-1.3} \label{eq:pwerlaw_cutoff} \end{split} \end{equation} where $m_{\rm wdm}$ is the cutoff mass, a characteristic of WDM scenarios, and the parameter $A$ is the normalization. We fit the parameterized WDM SHMF form to the data of the simulated galaxies, with the subhalos of the individual galaxies identified by \texttt{Rockstar}. We bin the identified subhalos in 15 mass bins, linearly spaced in logarithmic 10 base from $\log_{10}(M/M_\odot) = 7.75$ to $11$. The uncertainties in the observed subhalo counts $\hat{n}_i$ are dominated by Poisson noise, see Appendix~\ref{app:poisson}. To fit the parameters of~\ref{eq:pwerlaw_cutoff}, we use the likelihood defined in eqn~(\ref{eq:likelihood}) in Appendix~\ref{app:poisson}: \begin{equation} \ln\mathcal{L}(\hat{n}\mid\theta) = -\frac{1}{2}\sum_i \frac{\bigl(\hat{n}_i - n_i(\theta)\bigr)^2} {V_i \;-\; V'_i\,\bigl(\hat{n}_i - n_i(\theta)\bigr)}\, , \end{equation} where the index $i$ runs over the mass bins, $n_i(\theta)$ is the model prediction of eqn~(\ref{eq:pwerlaw_cutoff}), given the parameters $\theta = (A, m_{\mathrm{wdm}})$. We use the \texttt{emcee} package \cite{emcee_2013} to perform Markov Chain Monte Carlo (MCMC) sampling over this likelihood. This yields posterior samples for the amplitude $A$ and the WDM cutoff mass $m_{\rm wdm}$. We then use the samples $(A, m_{\rm wdm})$ obtained in this way to train a normalizing flow (NF), which allows us to account for correlations between $A$ and $m_{\rm wdm}$. Our goal is to then use this NF to predict the expected mass function at a given WDM mass of specific individual galaxies, and compare these predictions to observational constraints from other DM probes, such as strong gravitational lensing. For each zoom-in galaxy, we use 100 posterior samples from the fitted distribution of $(A, m_{\rm wdm})$ as training labels for the NF. This ensures that the NF learns the continuous distribution of plausible parameters for $A$ and $m_{\rm wdm}$, rather than a single point estimate. As the flowchart in Figure~\ref{fig:flow_architecture} illustrates, the MCMC samples are only used during training to help the NF learn the continuous distributions of $A$ and $m_{\rm wdm}$ conditioned on the galaxy morphologies and $M_{\rm DM}$. \subsection{Network Architecture and Training} Our architecture consists of two main components: a convolutional neural network (CNN) to process the image of the galaxy and a conditional normalizing flow (NF). Within a given cosmological model, the predicted SHMF depends on the properties of each individual galaxy. Given a WDM mass, our architecture infers the relation between the observable properties of the galaxies and their SHMF. Figure~\ref{fig:flow_architecture} shows a flowchart of the training and inference scheme we used. We first pre-train a ResNet-18 with a two-layer multi-layer perceptron (MLP) to predict the number of subhalos in the galaxy images, with the inverse WDM mass $M^{-1}_{\rm DM}$ concatenated to the first of the two MLP layers, using a mean squared error (MSE) loss. Our pretraining ensures a meaningful embedding space for the images, before using the output of the pretrained CNN as a condition for the NF. The embedded image and the inverse of the WDM mass $M^{-1}_{\rm DM}$ are used as conditions for a neural spline flow (NSF) to predict the parameters $A$ and $m_{\text{WDM}}$. We use the \texttt{zuko} library to implement the NSF \cite{Rozet_2022_zuko}. We use 730 of the zoom-in galaxies as training data and keep 85 as validation data, for both - the pretraining of the CNN and the training of the NSF - the same sets. To train the full model, all the weights of the ResNet are allowed to update, enabling end-to-end optimization of the feature extractor and density estimator. This allows us to efficiently model the posterior over the SHMF fit parameters conditioned on both the image and the WDM mass. \section{Results} \label{sec:Results} \begin{figure*}[th] \centering \vspace{-3mm} \includegraphics[width=0.33\textwidth]{Images/NF_comp/992_n.png} \includegraphics[width=0.33\textwidth]{Images/NF_comp/1015_n.png} \includegraphics[width=0.33\textwidth]{Images/NF_comp/1017_n.png} \includegraphics[width=0.33\textwidth]{Images/NF_comp/991_n.png} \includegraphics[width=0.33\textwidth]{Images/NF_comp/983_n.png} \includegraphics[width=0.33\textwidth]{Images/NF_comp/953_n.png} \vspace{-8.5mm} \caption{\textbf{The galaxy-specific halo mass functions under different cosmologies.} The figure shows the galaxy-specific halo mass functions for different WDM masses, with the corresponding galaxy image in the plot. The displayed galaxies come from three different WDM mass regions. The black dots are the counts of subhalos from the DREAMS simulation with Poisson uncertainties. The blue contours show the samples of the NF conditioned only on $M_{\rm DM}$, and the red contours the samples of the NF conditioned on both $M_{\rm DM}$ and the galaxy image. The NF conditioned only on $M_{\rm DM}$ shows a broader posterior range and bigger uncertainties on the fit.} \label{fig:NF_visual_comp} \vspace{-5mm} \end{figure*} Figure~\ref{fig:NF_visual_comp} shows galaxy-specific SHMFs with the corresponding galaxy image. We compare the NF conditioned on the galaxy images and $M_{\rm DM}$, and an NF conditioned only on $M_{\rm DM}$. This gives an estimate of how including the morphological information of the galaxy can improve the SHMF prediction, when compared to sampling a SHMF that has been marginalized over galaxy morphologies, as usually assumed from theoretical predictions. Since each galaxy was only simulated for a single WDM temperature in the DREAMS suite, Figure~\ref{fig:NF_visual_comp} performs this comparison for galaxies from the test set at a single WDM mass for each galaxy. We achieve an improvement in the SHMF predictions by including information about the galaxy morphology. The displayed galaxies come from three different WDM mass regions. The examples on the left come from higher WDM masses, the ones in the middle from medium masses, and the right side from low WDM masses. The black dots are the subhalo counts from the DREAMS simulations with Poisson uncertainties. The red and blue solid lines show the 50th percentile fit of the NF samples conditioned on the image and the samples of the NF only conditioned on $M_{\rm DM}$, respectively. The shaded regions show the $1\sigma$ and $2\sigma$ fits of the SHMF from eqn~\ref{eq:pwerlaw_cutoff} using the sampled parameters. The displayed contours show the $1\sigma$, $2\sigma$, and $3\sigma$ contours of the parameter samples $(A, m_{\rm wdm})$. The titles indicate the WDM mass range, which is passed along with the image to the neural network. For each range of $M_{\rm DM}$, we show two examples in the same column. The NF conditioned only on $M_{\rm DM}$ shows broader posteriors and larger uncertainties on the parameters of the SHMF. On the other hand, including the image information allows tighter constraints on both parameters, $A$ and $m_{\rm wdm}$, and highlights their correlations, resulting in tighter constraints on the SHMF. This supports the conclusion that incorporating galaxy images enables more precise predictions of the SHMF fit parameters than using the WDM mass $M_{\rm DM}$ alone. \begin{table}[t] \centering \vspace{-3mm} \caption{\textbf{PQMass-$\chi^2$ and RSME values}. The table shows the mean $\chi^2$ values obtained with PQMass, as well as the median RSME, for the NF conditioned on images and $M_{\rm DM}$, and an NF conditioned only on $M_{\rm DM}$ for the entire validation set. The comparison is made between the MCMC samples and the different NF samples for $A$ and $m_{\rm wdm}$.} \vspace{1mm} \begin{tabular}{l|c|c} \hline \hline & NF with image & NF without image \\ \hline PQM $\chi^2$ & $343.7\pm92.5$ & $385.8 \pm 121.7$ \\ Median RMSE & $0.26\pm 0.20$ & $0.55\pm0.17$ \\ \hline \hline \end{tabular} \vspace{-6mm} \label{tab:PQM} \end{table} We further test the NF conditioned on the galaxy images and $M_{\rm DM}$ against the NF only conditioned on $M_{\rm DM}$ qualitatively, to show that the inclusion of the galaxy images leads to a better performance of the NF. In Table~\ref{tab:PQM} we report the mean and standard deviation of the PQMass-$\chi^2$ values \citep{PQMass} for the entire validation set for the NF conditioned on images and $M_{\rm DM}$, and the NF only conditioned on $M_{\rm DM}$. We also report the median root mean squared error (RMSE) and its standard deviation of the entire validation set for both network cases. For that, we use for each condition the MCMC samples of the SHMF fit as target distribution and compare those against the NF samples of $A$ and $m_{\rm wdm}$. The closer the distributions are, the lower the PQMass-$\chi^2$ value. We do not expect the NF samples to match the MCMC fits perfectly, because each individual galaxy samples a distribution of possible SHMF for a given WDM model, making the inference under-specified without additional information. Providing additional galaxy images leads to a more informative inference of the possible SHMF, since they provide more constraining information. The lower RMSE value for the normalizing flow with access to the morphological information shows that the performance of the architecture improves and has tighter constraints on the SHMF. Additionally, we compare the MCMC fits of the SHMFs and the NF samples of the NF with image conditioning in Figure~\ref{fig:hmf_fits} in Appendix~\ref{app:NF_cond}. We do not compare the NF samples here with the MCMC samples, because the goal is to show that the NF with access to the image data does outperform the pure theoretical NF predictions based on the WDM only without image access. The current sample size of the simulation is too small to have a separate test set; therefore, we show the performance for the validation set. The provided examples show that the network is able to learn the galaxy-specific fit parameters within the predicted uncertainties. \section{Discussion} \label{sec:Discussion} Future iterations of this work will focus on increasing the realism of the input images and expanding the training dataset. The current images do not include the effects of dust attenuation, assume only Gaussian noise, and use a simplified Gaussian point spread function (PSF). Additionally, the images are expressed in flux units ($\mathrm{erg,s^{-1},Hz^{-1}}$) rather than in instrument-specific units. We plan to convert them to the native units of the Hubble Space Telescope (HST), i.e., $\mathrm{e^{-},s^{-1}}$, and to incorporate non-Gaussian, instrument-specific noise using SLIC \citep{Ronan_2023_SLIC}, along with more realistic PSF models. These improvements will be accompanied by the inclusion of the full set of \texttt{Rockstar} halo catalogs, including those for the remaining 209 DREAMS zoom-in simulations, to expand the training and validation sets and enable evaluation on an independent test set. The results demonstrate strong performance and highlight the potential of applying this architecture to more realistic simulations. However, there are important limitations to note regarding the training data. All galaxies used during training and validation are Milky Way-mass halos in isolated systems. This constraint is due to the availability of high-resolution DM zoom-in simulations, which currently exist only for these galaxy types, since running such detailed zoom-ins on cluster galaxies is computationally too expensive. Whilst the masses of the galaxies are for all galaxies in the order of the Milky Way, they are approximately equally distributed between spiral and elliptical galaxies. In contrast, strong gravitational lenses are more commonly observed to be massive galaxies in dense environments - often the central galaxies of clusters. These systems are not represented in the necessary mass resolutions in current hydrodynamical simulations. For these purposes, the subhalos should be resolved down to masses of $\log_{10}(M/M_\odot) = 7.75$ and below to be able to resolve small subhalos and confidently infer the SHMF. We expect that future high-resolution hydrodynamical simulations will model the relevant environments in greater detail, allowing us to extend the training set and improve generalization to observed lensing galaxies. Until then, our results should be interpreted within this limitation. \section*{Acknowledgements} This work is partially supported by Schmidt Sciences, a philanthropic initiative founded by Eric and Wendy Schmidt as part of the Virtual Institute for Astrophysics (VIA). The work is in part supported by computational resources provided by Calcul Quebec and the Digital Research Alliance of Canada. A.F. acknowledges the support from the Bourse J. Armand Bombardier and UdeM's final year scholarship. T.N. is supported by the CIERA Postdoctoral Fellowship. Y.H. and L.P. acknowledge support from the Canada Research Chairs Program, the National Sciences and Engineering Council of Canada through grants RGPIN-2020-05073 and 05102. \bibliography{bibliography} \bibliographystyle{icml2025} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % APPENDIX %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \newpage \appendix \onecolumn \section{Image Generation with Synthesizer} \label{app:synthesizer} \texttt{Synthesizer} produces galaxy images by generating spatially resolved spectral energy distributions (SEDs) and applying instrument-specific wavelength filters from the Spanish Virtual Observatory (SVO) filter service\footnote{\url{https://svo2.cab.inta-csic.es/theory/fps/}} \cite{Rodrigo_2012_SVO, Rodrigo_2020_SVO, Rodrigo_2024_SVO}. We use the Hubble Space Telescope Wide Field Camera (HST/WFC) F105W filter to simulate realistic near-infrared observations. The synthetic images are constructed by only taking stellar particles into account. We neglect the contributions of dust and gas particles, which are expected to have a relatively minor impact on the morphological features relevant to our analysis. In future steps, we will include the effects of dust and interstellar gas. As the first step of the image creation, we use an incident emission model and place the galaxies at redshift $z=0$. The particles are convolved with a smoothing filter for a more optical appealing visualization. The smoothing length of the individual stellar particles is taken for each particle from the simulation data directly, which means that any artifacts of isolated particles in the imaging are originating from the simulation. The smoothing length is the co-moving radius of the sphere centered on the particle enclosing the $32\pm1$ nearest particles of this same type. To ensure image fidelity, we first generate high-resolution images and convolve them at the high resolution with a Gaussian point spread function (PSF) to approximate observational effects. The PSF has a full-width half maximum of 3 pixels. The resulting images are then downsampled to a target resolution of 0.78125 kpc/pixel. We add gaussian noise of $10^{23} \frac{\rm erg}{\rm s \cdot Hz}$. We do not yet include instrument-specific observational noise or Poisson noise. Examples of the generated galaxy images are shown in Figure~\ref{fig:NF_visual_comp}, alongside the corresponding galaxy-specific SHMFs. \section{Poisson Noise from Samples} \label{app:poisson} To compute the Poisson noise of the counts of each bin of the SHMF, we use the \texttt{Rockstar} catalogs. We follow the prescription in \citet{Tanabashi_2018_Poisson, Chang_2021_poissonoise}. We compute the confidence intervals using the inverse cumulative distribution function of the $\chi^2$ distribution: \begin{align} \mu_{\rm lower} &= \frac{1}{2}\,F^{-1}_{\chi^2}\!\Bigl(\tfrac{\alpha}{2};\,2\hat{n}\Bigr) \\ \mu_{\rm higher} &= \frac{1}{2}\,F^{-1}_{\chi^2}\!\Bigl(1-\tfrac{\alpha}{2};\,2(\hat{n}+1)\Bigr) \label{eq:poisson_uncert} \end{align} with $F^{-1}_{\chi^2}$ the inverse of the $\chi^2$ cumulative distribution and $\hat{n}$ the number of counts. The confidence level is given by $100(1-\alpha)$. From these intervals, we define the asymmetric error bars and variances with: \begin{align} \sigma_{\mathrm{lower},i} &= \hat{n}_i \;-\;\mu_{\mathrm{lower},i}\\ \sigma_{\mathrm{higher},i} &= \mu_{\mathrm{higher},i}\;-\;\hat{n}_i\\ V_i &= \sigma_{\mathrm{lower},i}\,\sigma_{\mathrm{higher},i} \label{eq:v_i} \\ V'_i &= \sigma_{\mathrm{higher},i} \;-\;\sigma_{\mathrm{lower},i} \label{eq:V_i_prime} \end{align} We use the variances and uncertainties on the counts per bin to compute the likelihood of our fits to the data. The likelihood function to fit the SHMF (eqn~\ref{eq:pwerlaw_cutoff}) is defined by: \begin{equation} \ln\mathcal{L}(\hat{n}\mid\theta) = -\frac{1}{2}\sum_i \frac{\bigl(\hat{n}_i - n_i(\theta)\bigr)^2} {V_i \;-\; V'_i\,\bigl(\hat{n}_i - n_i(\theta)\bigr)} \label{eq:likelihood} \end{equation} where $n_i(\theta)$ is the model prediction of eqn~(\ref{eq:pwerlaw_cutoff}), given the parameters $\theta = (A, m_{\mathrm{wdm}})$. We use the likelihood function to fit the \texttt{Rockstar}-catalog data with an MCMC. \section{Comparison of Normalizing Flow Samples with MCMC Fits} \label{app:NF_cond} In Figure~\ref{fig:hmf_fits}, we show galaxy-specific SHMFs obtained by NF samples and MCMC fits along with the corresponding galaxy image. The figure is structured as Figure~\ref{fig:NF_visual_comp}. We use the same galaxies as before, but under different projections. We do not expect to perfectly recreate the MCMC fits. Our method serves as a tool to get the theoretical predictions on the SHMF given a WDM theory. This does not serve as constraints on the SHMF, but is rather to be used to compare theoretical predictions with observational constraints that can be achieved with strong lensing results. This is not a standalone method to learn about dark matter in observational surveys, but it needs a comparison counterpart that constrains the SHMF. The blue and red solid contours show the samples of the MCMC fit and of the NF samples, respectively. The dark and light shaded areas are the $1\sigma$ and $2\sigma$ regions of the fits. The displayed contours show the $1\sigma$, $2\sigma$, and $3\sigma$ contours of the MCMC fits and NF samples of $(A, m_{\rm wdm})$, defining the SHMF. The sampled parameters of the NF represent the fits obtained directly through the likelihood and cover the full range of the parameters sampled with MCMC. \begin{figure*}[ht] \centering \includegraphics[width=0.33\textwidth]{Images/992_mcmc.png} \includegraphics[width=0.33\textwidth]{Images/1015_mcmc.png} \includegraphics[width=0.33\textwidth]{Images/1017_mcmc.png} \includegraphics[width=0.33\textwidth]{Images/991_mcmc.png} \includegraphics[width=0.33\textwidth]{Images/983_mcmc.png} \includegraphics[width=0.33\textwidth]{Images/953_mcmc.png} % \vspace{-7mm} \caption{\textbf{Similar to Figure~\ref{fig:NF_visual_comp}.} The shown galaxies are the same as in Figure~\ref{fig:hmf_fits}, but the orientation of the galaxy images is different. The blue contours show the samples of the MCMC fit, and the red contours the samples of the NF conditioned on $M_{\rm DM}$ and the galaxy image. Overall, the sampled parameters of the NF represent the fits obtained directly through the likelihood and cover the full range of MCMC sampled parameters. } \label{fig:hmf_fits} % \vspace{-4mm} \end{figure*} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \end{document} ``` 4. **Bibliographic Information:** ```bbl \begin{thebibliography}{37} \providecommand{\natexlab}[1]{#1} \providecommand{\url}[1]{\texttt{#1}} \expandafter\ifx\csname urlstyle\endcsname\relax \providecommand{\doi}[1]{doi: #1}\else \providecommand{\doi}{doi: \begingroup \urlstyle{rm}\Url}\fi \bibitem[{Behroozi} et~al.(2013){Behroozi}, {Wechsler}, and {Wu}]{Behroozi_2013_Rockstar} {Behroozi}, P.~S., {Wechsler}, R.~H., and {Wu}, H.-Y. \newblock {The ROCKSTAR Phase-space Temporal Halo Finder and the Velocity Offsets of Cluster Cores}. \newblock \emph{\apj}, 762\penalty0 (2):\penalty0 109, January 2013. \newblock \doi{10.1088/0004-637X/762/2/109}. \bibitem[{Brehmer} et~al.(2019){Brehmer}, {Mishra-Sharma}, {Hermans}, {Louppe}, and {Cranmer}]{Brehmer_Sidd_2019_NRE} {Brehmer}, J., {Mishra-Sharma}, S., {Hermans}, J., {Louppe}, G., and {Cranmer}, K. \newblock {Mining for Dark Matter Substructure: Inferring Subhalo Population Properties from Strong Lenses with Machine Learning}. \newblock \emph{\apj}, 886\penalty0 (1):\penalty0 49, November 2019. \newblock \doi{10.3847/1538-4357/ab4c41}. \bibitem[{Brehmer} et~al.(2020){Brehmer}, {Louppe}, {Pavez}, and {Cranmer}]{brehmer2019mining} {Brehmer}, J., {Louppe}, G., {Pavez}, J., and {Cranmer}, K. \newblock Mining gold from implicit models to improve likelihood-free inference. \newblock \emph{Proceedings of the National Academy of Sciences}, 117\penalty0 (10):\penalty0 5242--5249, 2020. \newblock \doi{10.1073/pnas.1915980117}. \newblock URL \url{https://www.pnas.org/doi/abs/10.1073/pnas.1915980117}. \bibitem[{Chang} \& {Necib}(2021){Chang} and {Necib}]{Chang_2021_poissonoise} {Chang}, L.~J. and {Necib}, L. \newblock {Dark matter density profiles in dwarf galaxies: linking Jeans modelling systematics and observation}. \newblock \emph{\mnras}, 507\penalty0 (4):\penalty0 4715--4733, November 2021. \newblock \doi{10.1093/mnras/stab2440}. \bibitem[{Col{\'\i}n} et~al.(2000){Col{\'\i}n}, {Avila-Reese}, and {Valenzuela}]{Colin_2000_WDM} {Col{\'\i}n}, P., {Avila-Reese}, V., and {Valenzuela}, O. \newblock {Substructure and Halo Density Profiles in a Warm Dark Matter Cosmology}. \newblock \emph{\apj}, 542\penalty0 (2):\penalty0 622--630, October 2000. \newblock \doi{10.1086/317057}. \bibitem[Coogan et~al.(2022)Coogan, Montel, Karchev, Grootes, Nattino, and Weniger]{Coogan_2022} Coogan, A., Montel, N.~A., Karchev, K., Grootes, M.~W., Nattino, F., and Weniger, C. \newblock One never walks alone: the effect of the perturber population on subhalo measurements in strong gravitational lenses, 2022. \bibitem[{Diemand} et~al.(2007){Diemand}, {Kuhlen}, and {Madau}]{Diemand_2007_ViaLactea} {Diemand}, J., {Kuhlen}, M., and {Madau}, P. \newblock {Formation and Evolution of Galaxy Dark Matter Halos and Their Substructure}. \newblock \emph{\apj}, 667\penalty0 (2):\penalty0 859--877, October 2007. \newblock \doi{10.1086/520573}. \bibitem[{Ferreira}(2021)]{Ferreira_2021_DM} {Ferreira}, E. 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{Dvorkin}, C. \newblock {Subhalo effective density slope measurements from HST strong lensing data with neural likelihood-ratio estimation}. \newblock \emph{\mnras}, 527\penalty0 (2):\penalty0 4183--4192, January 2024. \newblock \doi{10.1093/mnras/stad3521}. \end{thebibliography} ``` 5. **Author Information:** - Lead Author: {'name': 'Andreas Filipp'} - Full Authors List: ```yaml Andreas Filipp: {} Tri Nguyen: {} Laurence Perreault-Levasseur: {} Jonah Rose: {} Chris Lovell: postdoc: start: 2025-07-17 thesis: null original_image: images/originals/chris_lovell.png image: /assets/group/images/chris_lovell.jpg Nicolas Payot: {} Francisco Villaescusa-Navarro: {} Yashar Hezaveh: {} ``` This YAML file provides a concise snapshot of an academic research group. It lists members by name along with their academic roles—ranging from Part III and summer projects to MPhil, PhD, and postdoctoral positions—with corresponding dates, thesis topics, and supervisor details. Supplementary metadata includes image paths and links to personal or departmental webpages. A dedicated "coi" section profiles senior researchers, highlighting the group’s collaborative mentoring network and career trajectories in cosmology, astrophysics, and Bayesian data analysis. ==================================================================================== Final Output Instructions ==================================================================================== - Combine all data sources to create a seamless, engaging narrative. - Follow the exact Markdown output format provided at the top. - Do not include any extra explanation, commentary, or wrapping beyond the specified Markdown. - Validate that every bibliographic reference with a DOI or arXiv identifier is converted into a Markdown link as per the examples. - Validate that every Markdown author link corresponds to a link in the author information block. - Before finalizing, confirm that no LaTeX citation commands or other undesired formatting remain. - Before finalizing, confirm that the link to the paper itself [2510.14766](https://arxiv.org/abs/2510.14766) is featured in the first sentence. Generate only the final Markdown output that meets all these requirements. {% endraw %}