Quantifying image distortions caused by strong gravitational lensing—the formation of multiple images of distant sources due to the deflection of their light by the gravity of intervening structures—and estimating the corresponding matter distribution of these structures (the ‘gravitational lens’) has primarily been performed using maximum likelihood modelling of observations. This procedure is typically time- and resource-consuming, requiring sophisticated lensing codes, several data preparation steps, and finding the maximum likelihood model parameters in a computationally expensive process with downhill optimizers1. Accurate analysis of a single gravitational lens can take up to a few weeks and requires expert knowledge of the physical processes and methods involved. Tens of thousands of new lenses are expected to be discovered with the upcoming generation of ground and space surveys2,3. Here we report the use of deep convolutional neural networks to estimate lensing parameters in an extremely fast and automated way, circumventing the difficulties that are faced by maximum likelihood methods. We also show that the removal of lens light can be made fast and automated using independent component analysis4 of multi-filter imaging data. Our networks can recover the parameters of the ‘singular isothermal ellipsoid’ density profile5, which is commonly used to model strong lensing systems, with an accuracy comparable to the uncertainties of sophisticated models but about ten million times faster: 100 systems in approximately one second on a single graphics processing unit. These networks can provide a way for non-experts to obtain estimates of lensing parameters for large samples of data.
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We thank R. Keisler, G. Holder, R. Blandford, R. Wechsler and W. Morningstar for discussions and comments on the manuscript. We also thank G. P. Maher and A. Dwaraknath for comments about neural networks, leading to improved performance. We thank Stanford Research Computing Center and their staff for providing computational resources (Sherlock Cluster) and support. Support for this work was provided by NASA through Hubble Fellowship grant HST-HF2-51358.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555. P.J.M. acknowledges support from the US Department of Energy under contract number DE-AC02-76SF00515. Y.D.H. is a Hubble Fellow.
The authors declare no competing financial interests.
Reviewer Information Nature thanks Y. Gal, A. Sonnenfeld and the other anonymous reviewer(s) for their contribution to the peer review of this work.
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Extended data figures and tables
Extended Data Figure 1 A selection of the test samples used to evaluate the performance of the network.
These examples are chosen to illustrate the variations of different effects, including cosmic rays (for example, panels 11 and 12), masks (for example, panels 6 and 23), Einstein radii (for example, panels 7 and 9), noise levels and PSF blurring strengths, and a mixture of lensing image configurations including some unfavourable morphologies (for example, panels 10 and 21).
For each row, the first two panels show the HST images in F475X and F600LP filters. The third and fourth columns show the outputs of the ICA. For comparison, lens-removed arcs using a Sérsic model are shown in the last column. Cosmic rays and the brightest central parts of the lensing galaxies have been masked.
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Hezaveh, Y., Levasseur, L. & Marshall, P. Fast automated analysis of strong gravitational lenses with convolutional neural networks. Nature 548, 555–557 (2017). https://doi.org/10.1038/nature23463
Reconstructing Functions and Estimating Parameters with Artificial Neural Networks: A Test with a Hubble Parameter and SNe Ia
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