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Here we present a machine learning framework and model implementation that can learn to simulate a wide variety of challenging physical domains, involving fluids, rigid solids, and deformable materials interacting with one another. Our framework—which we term “Graph Network-based Simulators” (GNS)—represents the state of a physical system with particles, expressed as nodes in a graph, and computes dynamics via learned message-passing. Our results show that our model can generalize from single-timestep predictions with thousands of particles during training, to different initial conditions, thousands of timesteps, and at least an order of magnitude more particles at test time. Our model was robust to hyperparameter choices across various evaluation metrics: the main determinants of long-term performance were the number of message-passing steps, and mitigating the accumulation of error by corrupting the training data with noise. Our GNS framework advances the state-of-the-art in learned physical simulation, and holds promise for solving a wide range of complex forward and inverse problems. 

We report the discovery of a complete Einstein ring around the elliptical galaxy NGC 6505, atz = 0.042. This is the first strong gravitational lens discovered inEuclidand the first in an NGC object from any survey. The combination of the low redshift of the lens galaxy, the brightness of the source galaxy (I_E = 18.1 lensed,I_E = 21.3 unlensed), and the completeness of the ring make this an exceptionally rare strong lens, unidentified until its observation byEuclid. We present deep imaging data of the lens from theEuclidVisible Camera (VIS) and Near-Infrared Spectrometer and Photometer (NISP) instruments, as well as resolved spectroscopy from theKeckCosmic Web Imager (KCWI). TheEuclidimaging in particular presents one of the highest signal-to-noise ratio optical/near-infrared observations of a strong gravitational lens to date. From the KCWI data we measure a source redshift ofz = 0.406. Using data from the Dark Energy Spectroscopic Instrument (DESI) we measure a velocity dispersion for the lens galaxy ofσ_⋆ = 303 ± 15 km s⁻¹. We model the lens galaxy light in detail, revealing angular structure that varies inside the Einstein ring. After subtracting this light model from the VIS observation, we model the strongly lensed images, finding an Einstein radius of 2.″5, corresponding to 2.1 kpc at the redshift of the lens. This is small compared to the effective radius of the galaxy,R_eff ∼ 12.″3. Combining the strong lensing measurements with analysis of the spectroscopic data we estimate a dark matter fraction inside the Einstein radius off_DM = (11.1_−3.5^+5.4)% and a stellar initial mass-function (IMF) mismatch parameter ofα_IMF = 1.26_−0.08^+0.05, indicating a heavier-than-Chabrier IMF in the centre of the galaxy.