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Dust grains absorb half of the radiation emitted by stars throughout the history of the universe, re-emitting this energy at infrared wavelengths. Polycyclic aromatic hydrocarbons (PAHs) are large organic molecules that trace millimeter-size dust grains and regulate the cooling of the interstellar gas within galaxies. Observations of PAH features in very distant galaxies have been difficult due to the limited sensitivity and wavelength coverage of previous infrared telescopes. Here we present JWST observations that detect the 3.3um PAH feature in a galaxy observed less than 1.5 billion years after the Big Bang. The high equivalent width of the PAH feature indicates that star formation, rather than black hole accretion, dominates the infrared emission throughout the galaxy. The light from PAH molecules, large dust grains, and stars and hot dust are spatially distinct from one another, leading to order-of-magnitude variations in the PAH equivalent width and the ratio of PAH to total infrared luminosity across the galaxy. The spatial variations we observe suggest either a physical offset between the PAHs and large dust grains or wide variations in the local ultraviolet radiation field. Our observations demonstrate that differences in the emission from PAH molecules and large dust grains are a complex result of localized processes within early galaxies., Comment: Published in Nature 5 June 2023 at https://www.nature.com/articles/s41586-023-05998-6. MIRI MRS reduction notebook is available at https://github.com/jwst-templates

Reconstructing the initial conditions of the universe is a key problem in cosmology. Methods based on simulating the forward evolution of the universe have provided a way to infer initial conditions consistent with present-day observations. However, due to the high complexity of the inference problem, these methods either fail to sample a distribution of possible initial density fields or require significant approximations in the simulation model to be tractable, potentially leading to biased results. In this work, we propose the use of score-based generative models to sample realizations of the early universe given present-day observations. We infer the initial density field of full high-resolution dark matter N-body simulations from the present-day density field and verify the quality of produced samples compared to the ground truth based on summary statistics. The proposed method is capable of providing plausible realizations of the early universe density field from the initial conditions posterior distribution marginalized over cosmological parameters and can sample orders of magnitude faster than current state-of-the-art methods., Comment: 8 pages, 7 figures

Likelihood analysis is typically limited to normally distributed noise due to the difficulty of determining the probability density function of complex, high-dimensional, non-Gaussian, and anisotropic noise. This is a major limitation for precision measurements in many domains of science, including astrophysics, for example, for the analysis of the Cosmic Microwave Background, gravitational waves, gravitational lensing, and exoplanets. This work presents Score-based LIkelihood Characterization (SLIC), a framework that resolves this issue by building a data-driven noise model using a set of noise realizations from observations. We show that the approach produces unbiased and precise likelihoods even in the presence of highly non-Gaussian correlated and spatially varying noise. We use diffusion generative models to estimate the gradient of the probability density of noise with respect to data elements. In combination with the Jacobian of the physical model of the signal, we use Langevin sampling to produce independent samples from the unbiased likelihood. We demonstrate the effectiveness of the method using real data from the Hubble Space Telescope and James Webb Space Telescope., Comment: 8 pages, 4 figures

Examining the detailed structure of galaxy populations provides valuable insights into their formation and evolution mechanisms. Significant barriers to such analysis are the non-trivial noise properties of real astronomical images and the point spread function (PSF) which blurs structure. Here we present a framework which combines recent advances in score-based likelihood characterization and diffusion model priors to perform a Bayesian analysis of image deconvolution. The method, when applied to minimally processed \emph{Hubble Space Telescope} (\emph{HST}) data, recovers structures which have otherwise only become visible in next-generation \emph{James Webb Space Telescope} (\emph{JWST}) imaging., Comment: 5+5 pages, 10 figures, Machine Learning and the Physical Sciences Workshop, NeurIPS 2023

Inferring accurate posteriors for high-dimensional representations of the brightness of gravitationally-lensed sources is a major challenge, in part due to the difficulties of accurately quantifying the priors. Here, we report the use of a score-based model to encode the prior for the inference of undistorted images of background galaxies. This model is trained on a set of high-resolution images of undistorted galaxies. By adding the likelihood score to the prior score and using a reverse-time stochastic differential equation solver, we obtain samples from the posterior. Our method produces independent posterior samples and models the data almost down to the noise level. We show how the balance between the likelihood and the prior meet our expectations in an experiment with out-of-distribution data., Comment: 5+6 pages, 3 figures, Accepted (poster + contributed talk) for the Machine Learning and the Physical Sciences Workshop at the 36th conference on Neural Information Processing Systems (NeurIPS 2022); Corrected style file and added authors checklist

We report the application of implicit likelihood inference to the prediction of the macro-parameters of strong lensing systems with neural networks. This allows us to perform deep learning analysis of lensing systems within a well-defined Bayesian statistical framework to explicitly impose desired priors on lensing variables, to obtain accurate posteriors, and to guarantee convergence to the optimal posterior in the limit of perfect performance. We train neural networks to perform a regression task to produce point estimates of lensing parameters. We then interpret these estimates as compressed statistics in our inference setup and model their likelihood function using mixture density networks. We compare our results with those of approximate Bayesian neural networks, discuss their significance, and point to future directions. Based on a test set of 100,000 strong lensing simulations, our amortized model produces accurate posteriors for any arbitrary confidence interval, with a maximum percentage deviation of $1.4\%$ at $21.8\%$ confidence level, without the need for any added calibration procedure. In total, inferring 100,000 different posteriors takes a day on a single GPU, showing that the method scales well to the thousands of lenses expected to be discovered by upcoming sky surveys., Comment: Accepted for publication in The Astrophysical Journal, 17 pages, 11 figures

Inferring accurate posteriors for high-dimensional representations of the brightness of gravitationally-lensed sources is a major challenge, in part due to the difficulties of accurately quantifying the priors. Here, we report the use of a score-based model to encode the prior for the inference of undistorted images of background galaxies. This model is trained on a set of high-resolution images of undistorted galaxies. By adding the likelihood score to the prior score and using a reverse-time stochastic differential equation solver, we obtain samples from the posterior. Our method produces independent posterior samples and models the data almost down to the noise level. We show how the balance between the likelihood and the prior meet our expectations in an experiment with out-of-distribution data., Comment: 5+6 pages, 3 figures, Accepted (poster + contributed talk) for the Machine Learning and the Physical Sciences Workshop at the 36th conference on Neural Information Processing Systems (NeurIPS 2022); Corrected style file and added authors checklist

A new generation of sky surveys is poised to provide unprecedented volumes of data containing hundreds of thousands of new strong lensing systems in the coming years. Convolutional neural networks are currently the only state-of-the-art method that can handle the onslaught of data to discover and infer the parameters of individual systems. However, many important measurements that involve strong lensing require population-level inference of these systems. In this work, we propose a hierarchical inference framework that uses the inference of individual lensing systems in combination with the selection function to estimate population-level parameters. In particular, we show that it is possible to model the selection function of a CNN-based lens finder with a neural network classifier, enabling fast inference of population-level parameters without the need for expensive Monte Carlo simulations., Comment: 8 pages, 5 figures, accepted at the ICML 2022 Workshop on Machine Learning for Astrophysics

In the coming years, a new generation of sky surveys, in particular, Euclid Space Telescope (2022), and the Rubin Observatory's Legacy Survey of Space and Time (LSST, 2023) will discover more than 200,000 new strong gravitational lenses, which represents an increase of more than two orders of magnitude compared to currently known sample sizes. Accurate and fast analysis of such large volumes of data under a statistical framework is therefore crucial for all sciences enabled by strong lensing. Here, we report on the application of simulation-based inference methods, in particular, density estimation techniques, to the predictions of the set of parameters of strong lensing systems from neural networks. This allows us to explicitly impose desired priors on lensing parameters, while guaranteeing convergence to the optimal posterior in the limit of perfect performance.

In the coming years, a new generation of sky surveys, in particular, Euclid Space Telescope (2022), and the Rubin Observatory's Legacy Survey of Space and Time (LSST, 2023) will discover more than 200,000 new strong gravitational lenses, which represents an increase of more than two orders of magnitude compared to currently known sample sizes. Accurate and fast analysis of such large volumes of data under a statistical framework is therefore crucial for all sciences enabled by strong lensing. Here, we report on the application of simulation-based inference methods, in particular, density estimation techniques, to the predictions of the set of parameters of strong lensing systems from neural networks. This allows us to explicitly impose desired priors on lensing parameters, while guaranteeing convergence to the optimal posterior in the limit of perfect performance., Comment: Accepted for the NeurIPS 2021 workshop Machine Learning and the Physical Sciences; 7 pages, 3 figures