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Machine learning methods are increasingly being employed as surrogate models in place of computationally expensive and slow numerical integrators for a bevy of applications in the natural sciences. However, while the laws of physics are relationships between scalars, vectors and tensors that hold regardless of the frame of reference or chosen coordinate system, surrogate machine learning models are not coordinate-free by default. We enforce coordinate freedom by using geometric convolutions in three model architectures: a ResNet, a Dilated ResNet and a UNet. In numerical experiments emulating two-dimensional compressible Navier–Stokes, we see better accuracy and improved stability compared with baseline surrogate models in almost all cases. The ease of enforcing coordinate freedom without making major changes to the model architecture provides an exciting recipe for any convolutional neural network-based method applied to an appropriate class of problems. 

Machine learning methods are increasingly being employed as surrogate models in place of computationally expensive and slow numerical integrators for a bevy of applications in the natural sciences. However, while the laws of physics are relationships between scalars, vectors and tensors that hold regardless of the frame of reference or chosen coordinate system, surrogate machine learning models are not coordinate-free by default. We enforce coordinate freedom by using geometric convolutions in three model architectures: a ResNet, a Dilated ResNet and a UNet. In numerical experiments emulating two-dimensional compressible Navier–Stokes, we see better accuracy and improved stability compared with baseline surrogate models in almost all cases. The ease of enforcing coordinate freedom without making major changes to the model architecture provides an exciting recipe for any convolutional neural network-based method applied to an appropriate class of problems. This article is part of the theme issue ‘Partial differential equations in data science’. 

Recent methods to simulate complex fluid dynamics problems have replaced computationally expensive and slow numerical integrators with surrogate models learned from data. However, while the laws of physics are relationships between scalars, vectors, and tensors that hold regardless of the frame of reference or chosen coordinate system, surrogate machine learning models are not coordinate-free by default. We enforce coordinate freedom by using geometric convolutions in three model architectures: a ResNet, a Dilated ResNet, and a UNet. In numerical experiments emulating 2D compressible Navier-Stokes, we see better accuracy and improved stability compared to baseline surrogate models in almost all cases. The ease of enforcing coordinate freedom without making major changes to the model architecture provides an exciting recipe for any CNN-based method applied on an appropriate class of problems. 

Abstract The changes in colors across a galaxy are intimately connected to the galaxy’s formation, growth, quenching history, and dust content. A particularly important epoch in the growth of galaxies is nearz∼ 2, often referred to as “cosmic noon,” where galaxies on average reach the peak of their star formation. We study a population of 125 cluster galaxies atz∼ 1.6 in three Hubble Space Telescope filters, F475W, F625W, and F160W, roughly corresponding to the rest-frame far-ultraviolet, near-ultraviolet, andrband, respectively. By comparing to a control sample of 200 field galaxies at similar redshift, we reveal clear, statistically significant differences in the overall spatially resolved colors and color gradients in galaxies across these two different environments. On average, cluster galaxies have redder ultraviolet colors in both the inner and outer regions bounded byr₅₀, as well as an overall wider dispersion of outside-in color gradients. The presence of these observed differences, along with evidence from ancillary data from previous studies, strongly suggests that the environment drives these population-level color differences, by affecting the stellar populations and/or dust content. 

Galaxy cluster mergers are representative of a wide range of physics, making them an excellent probe of the properties of dark matter and the ionized plasma of the intracluster medium. To date, most studies have focused on mergers occurring in the plane of the sky, where morphological features can be readily identified. To allow study of mergers with arbitrary orientation, we have assembled multi-probe data for the eight-cluster ICM-SHOX sample sensitive to both morphology and line of sight velocity. The first ICM-SHOX paper [1] provided an overview of our methodology applied to one member of the sample, MACS J0018.5+1626, in order to constrain its merger geometry. That work resulted in an exciting new discovery of a velocity space decoupling of its gas and dark matter distributions. In this work, we describe the availability and quality of multi-probe data for the full ICM-SHOX galaxy cluster sample. These datasets will form the observational basis of an upcoming full ICM-SHOX galaxy cluster sample analysis.