{% 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: "JAX-bandflux: differentiable supernovae SALT modelling for cosmological analysis on GPUs" date: 2025-04-10 categories: papers --- ![AI generated image](/assets/images/posts/2025-04-10-2504.08081.png) Samuel Alan Kossoff Leeney Content generated by [gemini-2.5-pro](https://deepmind.google/technologies/gemini/) using [this prompt](/prompts/content/2025-04-10-2504.08081.txt). Image generated by [imagen-4.0-generate-001](https://deepmind.google/technologies/gemini/) using [this prompt](/prompts/images/2025-04-10-2504.08081.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': 'Samuel Alan Kossoff Leeney'}). 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 [2504.08081](https://arxiv.org/abs/2504.08081) 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/2504.08081v1 guidislink: true link: https://arxiv.org/abs/2504.08081v1 title: 'JAX-bandflux: differentiable supernovae SALT modelling for cosmological analysis on GPUs' title_detail: !!python/object/new:feedparser.util.FeedParserDict dictitems: type: text/plain language: null base: '' value: 'JAX-bandflux: differentiable supernovae SALT modelling for cosmological analysis on GPUs' updated: '2025-04-10T19:22:11Z' updated_parsed: !!python/object/apply:time.struct_time - !!python/tuple - 2025 - 4 - 10 - 19 - 22 - 11 - 3 - 100 - 0 - tm_zone: null tm_gmtoff: null links: - !!python/object/new:feedparser.util.FeedParserDict dictitems: href: https://arxiv.org/abs/2504.08081v1 rel: alternate type: text/html - !!python/object/new:feedparser.util.FeedParserDict dictitems: href: https://arxiv.org/pdf/2504.08081v1 rel: related type: application/pdf title: pdf summary: JAX-bandflux is a JAX implementation of critical supernova modelling functionality for cosmological analysis. The codebase implements key components of the established library SNCosmo in a differentiable framework, offering efficient parallelisation and gradient-based optimisation capabilities through GPU acceleration. The package facilitates differentiable computation of supernova light curve measurements, supporting the inference of SALT parameters necessary for cosmological analysis. summary_detail: !!python/object/new:feedparser.util.FeedParserDict dictitems: type: text/plain language: null base: '' value: JAX-bandflux is a JAX implementation of critical supernova modelling functionality for cosmological analysis. The codebase implements key components of the established library SNCosmo in a differentiable framework, offering efficient parallelisation and gradient-based optimisation capabilities through GPU acceleration. The package facilitates differentiable computation of supernova light curve measurements, supporting the inference of SALT parameters necessary for cosmological analysis. tags: - !!python/object/new:feedparser.util.FeedParserDict dictitems: term: astro-ph.IM scheme: http://arxiv.org/schemas/atom label: null - !!python/object/new:feedparser.util.FeedParserDict dictitems: term: astro-ph.CO scheme: http://arxiv.org/schemas/atom label: null published: '2025-04-10T19:22:11Z' published_parsed: !!python/object/apply:time.struct_time - !!python/tuple - 2025 - 4 - 10 - 19 - 22 - 11 - 3 - 100 - 0 - tm_zone: null tm_gmtoff: null arxiv_comment: Submitted to The Journal of Open Source Software on 10th April 2025 arxiv_primary_category: term: astro-ph.IM authors: - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: Samuel Alan Kossoff Leeney author_detail: !!python/object/new:feedparser.util.FeedParserDict dictitems: name: Samuel Alan Kossoff Leeney author: Samuel Alan Kossoff Leeney ``` 3. **Paper Source (TeX):** ```tex \documentclass[10pt,a4paper,onecolumn]{article} \usepackage{marginnote} \usepackage{graphicx} \usepackage{xcolor} \usepackage{authblk,etoolbox} \usepackage{titlesec} \usepackage{calc} \usepackage{tikz} \usepackage{hyperref} \hypersetup{colorlinks,breaklinks, urlcolor=[rgb]{0.0, 0.5, 1.0}, linkcolor=[rgb]{0.0, 0.5, 1.0}} \usepackage{caption} \usepackage{tcolorbox} \usepackage{amssymb,amsmath} \usepackage{ifxetex,ifluatex} \usepackage{seqsplit} \usepackage{xstring} \usepackage{float} \let\origfigure\figure \let\endorigfigure\endfigure \renewenvironment{figure}[1][2] { \expandafter\origfigure\expandafter[H] } { \endorigfigure } \usepackage{fixltx2e} % provides \textsubscript \usepackage{natbib} \bibliographystyle{plainnat} % --- Splitting \texttt -------------------------------------------------- \let\textttOrig=\texttt \def\texttt#1{\expandafter\textttOrig{\seqsplit{#1}}} \renewcommand{\seqinsert}{\ifmmode \allowbreak \else\penalty6000\hspace{0pt plus 0.02em}\fi} % --- Pandoc does not distinguish between links like [foo](bar) and % --- [foo](foo) -- a simplistic Markdown model. However, this is % --- wrong: in links like [foo](foo) the text is the url, and must % --- be split correspondingly. % --- Here we detect links \href{foo}{foo}, and also links starting % --- with https://doi.org, and use path-like splitting (but not % --- escaping!) with these links. % --- Another vile thing pandoc does is the different escaping of % --- foo and bar. This may confound our detection. % --- This problem we do not try to solve at present, with the exception % --- of doi-like urls, which we detect correctly. \makeatletter \let\href@Orig=\href \def\href@Urllike#1#2{\href@Orig{#1}{\begingroup \def\Url@String{#2}\Url@FormatString \endgroup}} \def\href@Notdoi#1#2{\def\tempa{#1}\def\tempb{#2}% \ifx\tempa\tempb\relax\href@Urllike{#1}{#2}\else \href@Orig{#1}{#2}\fi} \def\href#1#2{% \IfBeginWith{#1}{https://doi.org}% {\href@Urllike{#1}{#2}}{\href@Notdoi{#1}{#2}}} \makeatother % --- Page layout ------------------------------------------------------------- \usepackage[top=3.5cm, bottom=3cm, right=1.5cm, left=1.0cm, headheight=2.2cm, reversemp, includemp, marginparwidth=4.5cm]{geometry} % --- Default font ------------------------------------------------------------ % \renewcommand\familydefault{\sfdefault} % --- Style ------------------------------------------------------------------- \renewcommand{\bibfont}{\small \sffamily} \renewcommand{\captionfont}{\small\sffamily} \renewcommand{\captionlabelfont}{\bfseries} % --- Section/SubSection/SubSubSection ---------------------------------------- \titleformat{\section} {\normalfont\sffamily\Large\bfseries} {}{0pt}{} \titleformat{\subsection} {\normalfont\sffamily\large\bfseries} {}{0pt}{} \titleformat{\subsubsection} {\normalfont\sffamily\bfseries} {}{0pt}{} \titleformat*{\paragraph} {\sffamily\normalsize} % --- Header / Footer --------------------------------------------------------- \usepackage{fancyhdr} \pagestyle{fancy} \fancyhf{} %\renewcommand{\headrulewidth}{0.50pt} \renewcommand{\headrulewidth}{0pt} \fancyhead[L]{\hspace{-0.75cm}} \fancyhead[C]{} \fancyhead[R]{} \renewcommand{\footrulewidth}{0.25pt} \fancyfoot[L]{\parbox[t]{0.98\headwidth}{\footnotesize{\sffamily , (). JAX-bandflux: differentiable supernovae SALT modelling for cosmological analysis on GPUs. \textit{}, (), . \url{https://doi.org/}}}} \fancyfoot[R]{\sffamily \thepage} \makeatletter \let\ps@plain\ps@fancy \fancyheadoffset[L]{4.5cm} \fancyfootoffset[L]{4.5cm} % --- Macros --------- \definecolor{linky}{rgb}{0.0, 0.5, 1.0} \newtcolorbox{repobox} {colback=red, colframe=red!75!black, boxrule=0.5pt, arc=2pt, left=6pt, right=6pt, top=3pt, bottom=3pt} \newcommand{\ExternalLink}{% \tikz[x=1.2ex, y=1.2ex, baseline=-0.05ex]{% \begin{scope}[x=1ex, y=1ex] \clip (-0.1,-0.1) --++ (-0, 1.2) --++ (0.6, 0) --++ (0, -0.6) --++ (0.6, 0) --++ (0, -1); \path[draw, line width = 0.5, rounded corners=0.5] (0,0) rectangle (1,1); \end{scope} \path[draw, line width = 0.5] (0.5, 0.5) -- (1, 1); \path[draw, line width = 0.5] (0.6, 1) -- (1, 1) -- (1, 0.6); } } % --- Title / Authors --------------------------------------------------------- % patch \maketitle so that it doesn't center \patchcmd{\@maketitle}{center}{flushleft}{}{} \patchcmd{\@maketitle}{center}{flushleft}{}{} % patch \maketitle so that the font size for the title is normal \patchcmd{\@maketitle}{\LARGE}{\LARGE\sffamily}{}{} % patch the patch by authblk so that the author block is flush left \def\maketitle{{% \renewenvironment{tabular}[2][] {\begin{flushleft}} {\end{flushleft}} \AB@maketitle}} \makeatletter \renewcommand\AB@affilsepx{ \protect\Affilfont} %\renewcommand\AB@affilnote[1]{{\bfseries #1}\hspace{2pt}} \renewcommand\AB@affilnote[1]{{\bfseries #1}\hspace{3pt}} \renewcommand{\affil}[2][]% {\newaffiltrue\let\AB@blk@and\AB@pand \if\relax#1\relax\def\AB@note{\AB@thenote}\else\def\AB@note{#1}% \setcounter{Maxaffil}{0}\fi \begingroup \let\href=\href@Orig \let\texttt=\textttOrig \let\protect\@unexpandable@protect \def\thanks{\protect\thanks}\def\footnote{\protect\footnote}% \@temptokena=\expandafter{\AB@authors}% {\def\\{\protect\\\protect\Affilfont}\xdef\AB@temp{#2}}% \xdef\AB@authors{\the\@temptokena\AB@las\AB@au@str \protect\\[\affilsep]\protect\Affilfont\AB@temp}% \gdef\AB@las{}\gdef\AB@au@str{}% {\def\\{, \ignorespaces}\xdef\AB@temp{#2}}% \@temptokena=\expandafter{\AB@affillist}% \xdef\AB@affillist{\the\@temptokena \AB@affilsep \AB@affilnote{\AB@note}\protect\Affilfont\AB@temp}% \endgroup \let\AB@affilsep\AB@affilsepx } \makeatother \renewcommand\Authfont{\sffamily\bfseries} \renewcommand\Affilfont{\sffamily\small\mdseries} \setlength{\affilsep}{1em} \ifnum 0\ifxetex 1\fi\ifluatex 1\fi=0 % if pdftex \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \else % if luatex or xelatex \ifxetex \usepackage{mathspec} \else \usepackage{fontspec} \fi \defaultfontfeatures{Ligatures=TeX,Scale=MatchLowercase} \fi % use upquote if available, for straight quotes in verbatim environments \IfFileExists{upquote.sty}{\usepackage{upquote}}{} % use microtype if available \IfFileExists{microtype.sty}{% \usepackage{microtype} \UseMicrotypeSet[protrusion]{basicmath} % disable protrusion for tt fonts }{} \usepackage{hyperref} \hypersetup{unicode=true, pdftitle={JAX-bandflux: differentiable supernovae SALT modelling for cosmological analysis on GPUs}, pdfborder={0 0 0}, breaklinks=true} \urlstyle{same} % don't use monospace font for urls % --- We redefined \texttt, but in sections and captions we want the % --- old definition \let\addcontentslineOrig=\addcontentsline \def\addcontentsline#1#2#3{\bgroup \let\texttt=\textttOrig\addcontentslineOrig{#1}{#2}{#3}\egroup} \let\markbothOrig\markboth \def\markboth#1#2{\bgroup \let\texttt=\textttOrig\markbothOrig{#1}{#2}\egroup} \let\markrightOrig\markright \def\markright#1{\bgroup \let\texttt=\textttOrig\markrightOrig{#1}\egroup} \IfFileExists{parskip.sty}{% \usepackage{parskip} }{% else \setlength{\parindent}{0pt} \setlength{\parskip}{6pt plus 2pt minus 1pt} } \setlength{\emergencystretch}{3em} % prevent overfull lines \providecommand{\tightlist}{% \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}} \setcounter{secnumdepth}{0} % Redefines (sub)paragraphs to behave more like sections \ifx\paragraph\undefined\else \let\oldparagraph\paragraph \renewcommand{\paragraph}[1]{\oldparagraph{#1}\mbox{}} \fi \ifx\subparagraph\undefined\else \let\oldsubparagraph\subparagraph \renewcommand{\subparagraph}[1]{\oldsubparagraph{#1}\mbox{}} \fi \title{JAX-bandflux: differentiable supernovae SALT modelling for cosmological analysis on GPUs} \author[1, 2]{Samuel Alan Kossoff Leeney} \affil[1]{Astrophysics Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, UK} \affil[2]{Kavli Institute for Cosmology, Madingley Road, Cambridge CB3 0HA, UK} \date{\vspace{-5ex}} \begin{document} \maketitle \marginpar{ \sffamily\small {\bfseries DOI:} \href{https://doi.org/}{\color{linky}{}} \vspace{2mm} {\bfseries Software} \begin{itemize} \setlength\itemsep{0em} \item \href{}{\color{linky}{Review}} \ExternalLink \item \href{}{\color{linky}{Repository}} \ExternalLink \item \href{}{\color{linky}{Archive}} \ExternalLink \end{itemize} \vspace{2mm} {\bfseries Submitted:} \\ {\bfseries Published:} \vspace{2mm} {\bfseries License}\\ Authors of papers retain copyright and release the work under a Creative Commons Attribution 4.0 International License (\href{https://creativecommons.org/licenses/by/4.0/}{\color{linky}{CC BY 4.0}}). } \section{Summary}\label{summary} \href{https://github.com/samleeney/JAX-bandflux}{JAX-bandflux} is a JAX \citep{jax2018github} implementation of critical supernova modelling functionality for cosmological analysis. The codebase implements key components of the established library SNCosmo \citep{barbary2016sncosmo} in a differentiable framework, offering efficient parallelisation and gradient-based optimisation capabilities through GPU acceleration. The package facilitates differentiable computation of supernova light curve measurements, supporting the inference of SALT \citep{kenworthy2021salt3, pierel2022salt3} parameters necessary for cosmological analysis. \section{Statement of need}\label{statement-of-need} Accurate estimation of supernova flux is essential in cosmological studies. These measurements are fundamental to the calibration of standard candles and subsequent distance determinations, which are used to answer cosmological questions. For example, the rate of expansion of the universe. Current packages such as SNCosmo \citep{barbary2016sncosmo} are widely used for analysing supernova data. However, traditional implementations are not designed to run on GPUs and they lack differentiability. A differentiable approach enables efficient gradient propagation during parameter optimisation and supports large-scale parallel computations on modern hardware such as GPUs. This JAX implementation addresses these requirements by providing differentiable, parallelisable routines for SALT parameter extraction. \section{Implementation}\label{implementation} The package is structured into several modules and example scripts that demonstrate various aspects of the supernova modelling workflow. Two primary example scripts, \texttt{fmin\_bfgs.py} and \texttt{ns.py}, illustrate optimisation via L-BFGS-B and nested sampling respectively. These scripts utilise core routines from the JAX modules, following a structure similar to SNCosmo while enabling differentiability and GPU acceleration. The central computation is contained in the file \texttt{salt3.py}, which implements the SALT3 model. The SALT model is of the form: \[ F(p, \lambda) = x_0 \left[ M_0(p, \lambda) + x_1 M_1(p, \lambda) + \ldots \right] \times \exp \left[ c \times CL(\lambda) \right] \] where free parameters are: \(x_0\), \(x_1\), \(t_0\), and \(c\). Model surface parameters are: \(M_0(p, \lambda)\) and \(M_1(p, \lambda)\) are functions that describe the underlying flux surfaces, and \(p\) is a function of redshift and \(t-2\). The computation of the bandflux is achieved by integrating the model flux across the applied bandpass filters. Combining multiple bands, the bandflux is defined as: \[ \text{bandflux} = \int_{\lambda_\text{min}}^{\lambda_\text{max}} F(\lambda) \cdot T(\lambda) \cdot \frac{\lambda}{hc} \, d\lambda \] Here, \(T(\lambda)\) is the transmission function specific to the bandpass filter used; \(h\) and \(c\) are the Planck constant and the speed of light respectively. Within \texttt{salt3.py}, the implementation computes the rest-frame model flux by combining the base spectral surface \(M_0(p, \lambda)\) with the stretch-modulated variation \(M_1(p, \lambda)\), each scaled by their respective SALT parameters. These operations utilise JAX's vectorised array manipulations, which are JIT-compiled for efficient, parallel execution on GPUs. The resulting flux is computed in a fully differentiable manner. The computed flux is then multiplied by the instrument's transmission function \(T(\lambda)\) and by the wavelength factor \(\lambda/(hc)\), followed by trapezoidal integration along the wavelength dimension using JAX's numerical integration capabilities. These operations are also JIT-compiled and can be parallelised across multiple data instances via \texttt{vmap}. The package includes comprehensive bandpass filter handling through the \texttt{bandpasses.py} module, which provides a \texttt{Bandpass} class to represent filter transmission functions. A set of commonly used astronomical filters is pre-integrated into the system, whilst additional custom bandpasses can be registered as needed through functions such as \texttt{register\_bandpass} and \texttt{load\_bandpass\_from\_file}. The system also facilitates the creation of bandpass objects from the Spanish Virtual Observatory (SVO) filter service. For data handling, the \texttt{data.py} module offers utilities for loading and processing supernova observations from various formats, including functions to handle redshift data and prepare it for model fitting. The package currently supports both SALT3 and SALT3-NIR models through dedicated interpolation routines found in \texttt{salt3.py}. This architecture allows gradient propagation through the entire analysis pipeline, enabling techniques that benefit from JAX's differentiable, parallelisable programming paradigm. The implementation maintains functional parity with SNCosmo whilst providing an enhanced computational efficiency and scalability for contemporary cosmological analyses. \bibliography{paper.bib} \end{document} ``` 4. **Bibliographic Information:** ```bbl \begin{thebibliography}{4} \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[Barbary et~al.(2016)Barbary, Barclay, Biswas, Craig, Feindt, Friesen, Goldstein, Jha, Rodney, Sofiatti, et~al.]{barbary2016sncosmo} Kyle Barbary, Tom Barclay, Rahul Biswas, Matt Craig, Ulrich Feindt, Brian Friesen, Danny Goldstein, Saurabh Jha, Steve Rodney, Caroline Sofiatti, et~al. \newblock Sncosmo: Python library for supernova cosmology. \newblock \emph{Astrophysics Source Code Library}, pages ascl--1611, 2016. \bibitem[Bradbury et~al.(2018)Bradbury, Frostig, Hawkins, Johnson, Leary, Maclaurin, Necula, Paszke, Vander{P}las, Wanderman-{M}ilne, and Zhang]{jax2018github} James Bradbury, Roy Frostig, Peter Hawkins, Matthew~James Johnson, Chris Leary, Dougal Maclaurin, George Necula, Adam Paszke, Jake Vander{P}las, Skye Wanderman-{M}ilne, and Qiao Zhang. \newblock {JAX}: composable transformations of {P}ython+{N}um{P}y programs, 2018. \newblock URL \url{http://github.com/jax-ml/jax}. \bibitem[Kenworthy et~al.(2021)Kenworthy, Jones, Dai, Kessler, Scolnic, Brout, Siebert, Pierel, Dettman, Dimitriadis, et~al.]{kenworthy2021salt3} WD~Kenworthy, DO~Jones, M~Dai, R~Kessler, D~Scolnic, D~Brout, MR~Siebert, JDR Pierel, KG~Dettman, G~Dimitriadis, et~al. \newblock Salt3: An improved type ia supernova model for measuring cosmic distances. \newblock \emph{The Astrophysical Journal}, 923\penalty0 (2):\penalty0 265, 2021. \bibitem[Pierel et~al.(2022)Pierel, Jones, Kenworthy, Dai, Kessler, Ashall, Do, Peterson, Shappee, Siebert, et~al.]{pierel2022salt3} JDR Pierel, DO~Jones, WD~Kenworthy, M~Dai, R~Kessler, C~Ashall, A~Do, ER~Peterson, BJ~Shappee, MR~Siebert, et~al. \newblock Salt3-nir: Taking the open-source type ia supernova model to longer wavelengths for next-generation cosmological measurements. \newblock \emph{The Astrophysical Journal}, 939\penalty0 (1):\penalty0 11, 2022. \end{thebibliography} ``` 5. **Author Information:** - Lead Author: {'name': 'Samuel Alan Kossoff Leeney'} - Full Authors List: ```yaml Samuel Alan Kossoff Leeney: phd: start: 2023-10-01 supervisors: - Eloy de Lera Acedo - Harry Bevins - Will Handley thesis: null mphil: start: 2022-04-11 end: 2022-12-30 supervisors: - Eloy de Lera Acedo thesis: 'Data science in early universe Cosmology: a novel Bayesian RFI mitigation approach using numerical sampling techniques' original_image: images/originals/sam_leeney.jpeg image: /assets/group/images/sam_leeney.jpg links: Webpage: https://github.com/samleeney Group Webpage: https://www.cavendishradiocosmology.com/ ``` 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 [2504.08081](https://arxiv.org/abs/2504.08081) is featured in the first sentence. Generate only the final Markdown output that meets all these requirements. {% endraw %}