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Being able to quantify uncertainty when comparing a theoretical or computational model to observations is critical to conducting a sound scientific investigation. With the rise of data-driven modelling, understanding various sources of uncertainty and developing methods to estimate them has gained renewed attention. Five researchers discuss uncertainty quantification in machine-learned models with an emphasis on issues relevant to physics problems.Five researchers discuss uncertainty quantification in machine-learned models with an emphasis on issues relevant to physics problems.

With the advent of wide-field surveys, cosmology has entered a new golden age of data where our cosmological model and the nature of dark universe will be tested with unprecedented accuracy, so that we can strive for high precision cosmology. Observational probes like weak lensing, galaxy surveys and the cosmic microwave background as well as other observations will all contribute to these advances. These different probes trace the underlying expansion history and growth of structure in complementary ways and can be combined in order to extract cosmological parameters as best as possible. With future wide-field surveys, observational overlap means these will trace the same physical underlying dark matter distribution, and extra care must be taken when combining information from different probes. Consideration of probe combination is a fundamental aspect of cosmostatistics and important to ensure optimal use of future wide-field surveys.

Using the 3D information provided by photometric or spectroscopic weak lensing surveys, it has become possible in the last few years to address the problem of mapping the matter density contrast in three dimensions from gravitational lensing. We recently proposed a new non linear sparsity based reconstruction method allowing for high resolution reconstruction of the over-density. This new technique represents a significant improvement over previous linear methods and opens the way to new applications of 3D weak lensing density reconstruction. In particular, we demonstrate that for the first time reconstructed over-density maps can be used to detect and characterise galaxy clusters in mass and redshift.

Forthcoming cosmological imaging surveys, such as the Rubin Observatory LSST, require large-scale simulations encompassing realistic galaxy populations for a variety of scientific applications. Of particular concern is the phenomenon of intrinsic alignments (IA), whereby galaxies orient themselves towards overdensities, potentially introducing significant systematic biases in weak gravitational lensing analyses if they are not properly modeled. Due to computational constraints, simulating the intricate details of galaxy formation and evolution relevant to IA across vast volumes is impractical. As an alternative, we propose a Deep Generative Model trained on the IllustrisTNG-100 simulation to sample 3D galaxy shapes and orientations to accurately reproduce intrinsic alignments along with correlated scalar features. We model the cosmic web as a set of graphs, each graph representing a halo with nodes representing the subhalos/galaxies. The architecture consists of a SO(3) \\(\\times\\) \\(\\mathbb{R}^n\\) diffusion generative model, for galaxy orientations and \\(n\\) scalars, implemented with E(3) equivariant Graph Neural Networks that explicitly respect the Euclidean symmetries of our Universe. The model is able to learn and predict features such as galaxy orientations that are statistically consistent with the reference simulation. Notably, our model demonstrates the ability to jointly model Euclidean-valued scalars (galaxy sizes, shapes, and colors) along with non-Euclidean valued SO(3) quantities (galaxy orientations) that are governed by highly complex galactic physics at non-linear scales.

Low surface brightness substructures around galaxies, known as tidal features, are a valuable tool in the detection of past or ongoing galaxy mergers, and their properties can answer questions about the progenitor galaxies involved in the interactions. The assembly of current tidal feature samples is primarily achieved using visual classification, making it difficult to construct large samples and draw accurate and statistically robust conclusions about the galaxy evolution process. With upcoming large optical imaging surveys such as the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST), predicted to observe billions of galaxies, it is imperative that we refine our methods of detecting and classifying samples of merging galaxies. This paper presents promising results from a self-supervised machine learning model, trained on data from the Ultradeep layer of the Hyper Suprime-Cam Subaru Strategic Program optical imaging survey, designed to automate the detection of tidal features. We find that self-supervised models are capable of detecting tidal features, and that our model outperforms previous automated tidal feature detection methods, including a fully supervised model. An earlier method applied to real galaxy images achieved 76% completeness for 22% contamination, while our model achieves considerably higher (96%) completeness for the same level of contamination. We emphasise a number of advantages of self-supervised models over fully supervised models including maintaining excellent performance when using only 50 labelled examples for training, and the ability to perform similarity searches using a single example of a galaxy with tidal features.

Diffusion-based generative models represent the current state-of-the-art for image generation. However, standard diffusion models are based on Euclidean geometry and do not translate directly to manifold-valued data. In this work, we develop extensions of both score-based generative models (SGMs) and Denoising Diffusion Probabilistic Models (DDPMs) to the Lie group of 3D rotations, SO(3). SO(3) is of particular interest in many disciplines such as robotics, biochemistry and astronomy/cosmology science. Contrary to more general Riemannian manifolds, SO(3) admits a tractable solution to heat diffusion, and allows us to implement efficient training of diffusion models. We apply both SO(3) DDPMs and SGMs to synthetic densities on SO(3) and demonstrate state-of-the-art results. Additionally, we demonstrate the practicality of our model on pose estimation tasks and in predicting correlated galaxy orientations for astrophysics/cosmology.

As the volume and quality of modern galaxy surveys increase, so does the difficulty of measuring the cosmological signal imprinted in galaxy shapes. Weak gravitational lensing sourced by the most massive structures in the Universe generates a slight shearing of galaxy morphologies called cosmic shear, key probe for cosmological models. Modern techniques of shear estimation based on statistics of ellipticity measurements suffer from the fact that the ellipticity is not a well-defined quantity for arbitrary galaxy light profiles, biasing the shear estimation. We show that a hybrid physical and deep learning Hierarchical Bayesian Model, where a generative model captures the galaxy morphology, enables us to recover an unbiased estimate of the shear on realistic galaxies, thus solving the model bias.

Low surface brightness substructures around galaxies, known as tidal features, are a valuable tool in the detection of past or ongoing galaxy mergers. Their properties can answer questions about the progenitor galaxies involved in the interactions. This paper presents promising results from a self-supervised machine learning model, trained on data from the Ultradeep layer of the Hyper Suprime-Cam Subaru Strategic Program optical imaging survey, designed to automate the detection of tidal features. We find that self-supervised models are capable of detecting tidal features and that our model outperforms previous automated tidal feature detection methods, including a fully supervised model. The previous state of the art method achieved 76% completeness for 22% contamination, while our model achieves considerably higher (96%) completeness for the same level of contamination.

The intracluster light (ICL) is an important tracer of a galaxy cluster's history and past interactions. However, only small samples have been studied to date due to its very low surface brightness and the heavy manual involvement required for the majority of measurement algorithms. Upcoming large imaging surveys such as the Vera C. Rubin Observatory's Legacy Survey of Space and Time are expected to vastly expand available samples of deep cluster images. However, to process this increased amount of data, we need faster, fully automated methods to streamline the measurement process. This paper presents a machine learning model designed to automatically measure the ICL fraction in large samples of images, with no manual preprocessing required. We train the fully supervised model on a training dataset of 50,000 images with injected artificial ICL profiles. We then transfer its learning onto real data by fine-tuning with a sample of 101 real clusters with their ICL fraction measured manually using the surface brightness threshold method. With this process, the model is able to effectively learn the task and then adapt its learning to real cluster images. Our model can be directly applied to Hyper Suprime-Cam images, processing up to 500 images in a matter of seconds on a single GPU, or fine-tuned for other imaging surveys such as LSST, with the fine-tuning process taking just 3 minutes. The model could also be retrained to match other ICL measurement methods. Our model and the code for training it is made available on GitHub.

We develop a transformer-based conditional generative model for discrete point objects and their properties. We use it to build a model for populating cosmological simulations with gravitationally collapsed structures called dark matter halos. Specifically, we condition our model with dark matter distribution obtained from fast, approximate simulations to recover the correct three-dimensional positions and masses of individual halos. This leads to a first model that can recover the statistical properties of the halos at small scales to better than 3% level using an accelerated dark matter simulation. This trained model can then be applied to simulations with significantly larger volumes which would otherwise be computationally prohibitive with traditional simulations, and also provides a crucial missing link in making end-to-end differentiable cosmological simulations. The code, named GOTHAM (Generative cOnditional Transformer for Halo's Auto-regressive Modeling) is publicly available at https://github.com/shivampcosmo/GOTHAM.