Neural Networks  collection of links
Links to tools
deeplearning.net is a great source of links for various DNN tools. TensorHub collects models, data sets, solutions and other resources. Current tool of choice is the TensorFlow.
List of potentially interesting use of artificial neural networks in astronomy

Skynet (ANSII C, MPI): SKYNET: an efficient and robust neural network training tool for machine learning in astronomy https://arxiv.org/abs/1309.0790

GUANGTUN BEN ZHU, PhD  tools for cosmology http://www.guangtunbenzhu.com/#!deeplearning/stoom https://github.com/guangtunbenzhu/BGTCosmology (BGT  Bimetric Gravity Theory?)

Measuring photometric redshifts using galaxy images and Deep Neural Networks. Tree methods and lenet (convolutional neural networks) http://adsabs.harvard.edu/abs/2016A%26C….16…34H

Deep Learning Approach for Classifying Galaxies. Convolutional neural networks http://ijarcsse.com/docs/papers/Volume_6/4_April2016/V6I40340.pdf

Galaxy Zoo Challenge: Classify Galaxy Morphologies from Images. PCA (Principle Component Analysis), SIFT (ScaleInvariant Feature Transform), HOG (Histogram of Oriented Gradients) http://web.stanford.edu/class/cs231a/prev_projects/C231a_final.pdf

Rotationinvariant convolutional neural networks for galaxy morphology prediction https://arxiv.org/pdf/1503.07077.pdf http://blog.kaggle.com/2014/04/18/winningthegalaxychallengewithconvnets/

Proposal to classify 100 mln galaxies: http://pleiades.ucsc.edu/ams250/projects/Note_Google_proposal_Mar3_2016.pdf A Catalog of VisualLike Morphologies in the 5 CANDELS Fields Using Deep Learning

GPU days 2016, Wigner Center Applications of GPUaccelerated deep neural networks to analyze galaxy spectra http://indico.kfki.hu/event/387/contribution/10

Not a DNN, but Generative Artificial NN (GANN) applied for Gaia spectra. On the estimation of stellar parameters with uncertainty prediction from Generative Artificial Neural Networks: application to Gaia RVS simulated spectra