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Cosmic shear is a primary cosmological probe for several present and upcomingsurveys investigating dark matter and dark energy, such as Euclid or WFIRST.The probe requires an extremely accurate measurement of the shapes of millionsof galaxies based on imaging data. Crucially, the shear measurement mustaddress and compensate for a range of interwoven nuisance effects related tothe instrument optics and detector, noise, unknown galaxy morphologies, colors,blending of sources, and selection effects. This paper explores the use ofsupervised machine learning (ML) as a tool to solve this inverse problem. Wepresent a simple architecture that learns to regress shear point estimates andweights via shallow artificial neural networks. The networks are trained onsimulations of the forward observing process, and take combinations of momentsof the galaxy images as inputs. A challenging peculiarity of this MLapplication is the combination of the noisiness of the input features and therequirements on the accuracy of the inverse regression. To address this issue,the proposed training algorithm minimizes bias over multiple realizations ofindividual source galaxies, reducing the sensitivity to properties of theoverall sample of source galaxies. Importantly, an observational selectionfunction of these source galaxies can be straightforwardly taken into accountvia the weights. We first introduce key aspects of our approach using toy-modelsimulations, and then demonstrate its potential on images mimicking Eucliddata. Finally, we analyze images from the GREAT3 challenge, obtainingcompetitively low shear biases despite the use of a simple training set. Weconclude that the further development of ML approaches is of high interest tomeet the stringent requirements on the shear measurement in current and futuresurveys. A demonstration implementation of our technique is publicly available.

Weak-lensing shear measurement with machine learning: teaching artificial neural networks about feature noise