A neural network gravitational arc finder based on the Mediatrix filamentation method

Abstract

Context. Automated arc detection methods are needed to scan the ongoing and next-generation wide-field imaging surveys, which are expected to contain thousands of strong lensing systems. Arc finders are also required for a quantitative comparison between predictions and observations of arc abundance. Several algorithms have been proposed to this end, but machine learning methods have remained as a relatively unexplored step in the arc finding process. Aims. In this work we introduce a new arc finder based on pattern recognition, which uses a set of morphological measurements that are derived from the Mediatrix filamentation method as entries to an artificial neural network (ANN). We show a full example of the application of the arc finder, first training and validating the ANN on simulated arcs and then applying the code on four Hubble Space Telescope (HST) images of strong lensing systems. Methods. The simulated arcs use simple prescriptions for the lens and the source, while mimicking HST observational conditions. We also consider a sample of objects from HST images with no arcs in the training of the ANN classification. We use the training and validation process to determine a suitable set of ANN configurations, including the combination of inputs from the Mediatrix method, so as to maximize the completeness while keeping the false positives low. Results. In the simulations the method was able to achieve a completeness of about 90% with respect to the arcs that are input into the ANN after a preselection. However, this completeness drops to ∼70% on the HST images. The false detections are on the order of 3% of the objects detected in these images. Conclusions. The combination of Mediatrix measurements with an ANN is a promising tool for the pattern-recognition phase of arc finding. More realistic simulations and a larger set of real systems are needed for a better training and assessment of the efficiency of the method.

Identifying strong lenses with unsupervised machine learning using convolutional autoencoder

“…We have three dense layers (units: 32, 64, and 128), five convolutional layers (filter sizes: 8, 16, 32, 64, and 128) using the ReLu activation function (Nair & Hinton 2010), and an extra convolutional layer (filter: 1) using the softmax function (Bishop 2006), f (z) = exp (z)/ exp z j , as the output for the decoder. Each convolutional layer apart from the last layer (output) is followed with an upsampling layer which has the opposite function to the pooling layer that is used for recovering the resolution.…”

“…The Bayesian Gaussian mixture model (BGM) is a variational Gaussian mixture model (Kullback & Leibler 1951;Attias 2000;Bishop 2006) which maximises the evidence lower bound (ELBO) (Kullback & Leibler 1951) in the loglikelihood. In this study, we apply the BGM from the scikitlearn library 3 (Pedregosa et al 2011).…”

“…To this end, a number of algorithms have been developed to detect GGSLs in image data by recognising arclike features and Einstein rings (e.g. Gavazzi et al 2014;Joseph et al 2014;Paraficz et al 2016;Bom et al 2017). In addition, instead of recognising arc-like features, an alternative detection technique that has had some success is to attempt to fit lens mass models to candidate GGSLs and reject those systems that do not converge (Marshall et al 2009;Sonnenfeld & Leauthaud 2018).…”

“…The application of CNNs for detecting these GGSL systems has reached a high success rate in binary classification (Jacobs et al 2017;Petrillo et al 2017;Ostrovski et al 2017;Bom et al 2017;Hartley et al 2017;Avestruz et al 2019;Lanusse et al 2018); however, the application of supervised machine learning such as CNNs is prone to human bias and training set bias which may not properly represent the diversity of real GGSL systems observed in future surveys. Additionally, GGSLs are rare events in the Universe so that there is insufficiently homogeneous data for training in supervised machine learning methods.…”

Derivation of NARX models by expanding activation functions in neural networks

“…Chen et al [3] and Levin and Narendra [4] demonstrated that nonlinear systems can be identified using neural networks. Furthermore, free open-source libraries such as the Fast Artificial Neural Network Library (FANN) [5] for network learning have already enabled researchers in various fields to use neural networks [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. In fact, neural networks have recently been used for the identification of a wide range of nonlinear systems, including biological systems [23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”