SELECTION OF STRONG GRAVITATIONAL LENSES WITH CONVOLUTIONAL NEURAL NETWORKS
ENRICO PETRILLO
PROF. DR. L.V.E. KOOPMANSDR. G. VERDOES KLEIJN
S. CHATTERJEEDR. C. TORTORA
DR. G. VERNARDOS
COSMO2125/5/2016
STRONG GRAVITATIONAL LENSING
STRONG GRAVITATIONAL LENSING
Scientific applications:
• Hubble Constant.
• Dark energy.
• Stellar and dark matter distribution in inner regions of galaxies.
• Magnified view of distant objects.
Accuracy relies strongly on the numberof lens systems. ~700 systems known so far from different surveys.
THE KILO DEGREE SURVEY (KIDS)
• 1500 square degrees in u, g, r, i filters.
• 2 mags deeper than SDSS.
• r-band seeing 0.65’’.
• Pixel scale 0.21’’/pixel.
Located at ESO’s La Silla Paranal Observatory, Cerro Paranal (Chile)
THE KILO DEGREE SURVEY (KIDS)
• 1500 square degrees in u, g, r, i filters.
• 2 mags deeper than SDSS.
• r-band seeing 0.65’’.
• Pixel scale 0.21’’/pixel.
SDSS KiDS
EXPECTED NUMBER OF LENSES
Now KiDS EUCLID
~700 ~1500 ~105
From simple lensing statistics.See, e.g., Pawase et al. 2012.
KIDS
HOW TO FIND THEM?
HOW TO FIND THEM?
• VISUAL INSPECTION
HOW TO FIND THEM?
• VISUAL INSPECTION
HOW TO FIND THEM?
• VISUAL INSPECTION
• AUTOMATED METHODS
HOW TO FIND THEM?
• VISUAL INSPECTION
• AUTOMATED METHODS
HOW TO FIND THEM?
• VISUAL INSPECTION
• AUTOMATED METHODS
Convolutional Neural Networks (ConvNets) are a
powerful algorithm for pattern recognition.
They have been used extensively in industry and
academia performing better than humans in
many tasks.
http://www.tensorflow.orgGoogle’s library for
Machine Intelligence.
WHAT ARE NEURAL NETWORKS?
Linear
Non-Linear
Data Parameters:Weights and biases
𝑓3(∑𝑤3𝑖𝑥𝑖 + 𝑏3)
𝑓1(∑𝑤1𝑖𝑥𝑖 + 𝑏1)
𝑓2(∑𝑤2𝑖𝑥𝑖 + 𝑏2)𝑓(∑𝑤𝑖𝑓𝑖 + 𝑏)
𝑓𝑛(∑𝑤𝑛𝑖𝑥𝑖 + 𝑏𝑛)
Object class
The classifier is built choosing the parameters W and b and the network architecture.
DATA !
NEURAL NETWORK
e.g., 𝑓 𝑥 = max(0, 𝑥)
HOW TO SET THE PARAMETERS (TRAINING)
• Minimizing a Loss Function 𝐿(𝑜𝑢𝑡𝑝𝑢𝑡, 𝑟𝑒𝑎𝑙_𝑣𝑎𝑙𝑢𝑒).
• Taking the gradient of L with respect to the parametersand update them in the negative gradient direction.
• By changing the parameters, data point by data point, the network learns the classification.
From http://playground.tensorflow.org/
WHEN INPUTS ARE IMAGES
Use as input some specific features.
E.g., ellipticity, Kron radius, etc.
Using the pixel values.
But too many parameters and risk to over-fit!
E.g., 100x100 pixels => 10.000 parameters per neuron!
CONVOLUTIONAL NETWORKS
Convolution filters:
• Locally connected. • Swipe the whole image with the same weights. • Every filter learns a feature and creates a feature map.
ConvNets can be seen as feature extractors!
CONVOLUTIONAL NETWORKS
Pooling layers:
• Down-sample the feature maps. • Reduce the number of the free parameters.• Create a sort of translational invariance.
CONVOLUTIONAL NETWORKS
Pooling layers:
• Down-sample the feature maps. • Reduce the number of the free parameters.• Create a sort of translational invariance.
TRAINING THE NETWORK
• This kind of network needs a large dataset in order to learn the classification.
• Such a “training set” for gravitational lenses is still not available!
• Mock data are needed to train the network.
MOCK DATA PRODUCTION
Blue background source lensed by Early Type Galaxy is the most likely configuration.
106 simulationswith different
configurations of the physical parameters.
~6000 KiDS LRGs selected with
Eisenstein et al. (2001) color cut.
With data augmentation we can produce mock images
ad libitum.
MOCK DATA PRODUCTION
20 arcsec
AFTER TRAINING ON 5 × 106 EXAMPLES
Some first layer filters learned by the network. They are actually searching for particular patterns.
RESULTS (WORK IN PROGRESS)
Validation on 2000 simulated sources:Completeness 94%Purity 98%
With real data we see that there is contamination from arc-like sources.
Retraining the network adding the false positives improves the classification.
RESULTS (WORK IN PROGRESS)
From a sample of 80.000 real galaxies the network selects 2,4% candidates.
We need to evaluate the purity by visual inspection.
Visual inspection is still needed
Visual inspection is still needed
But we need fewer monkeys!
NEXT STEPS AND CONCLUSIONS
• Improving the CNN selection with a larger training set.
• Using multiband information.
• Model averaging.
• We are going to apply it to the first KiDS 400 square degrees.
• Complete overlap with infrared counterpart VIKING.
• Overlap with 2dF and 2dFLenS.
• NGP stripe overlaps UKIDSS, Sloan, GAMA-1.
• SGP stripe overlaps DES, GAMA-2.
• Optimal for Southern follow-up:
VLT, ALMA, etc.
THE KILO DEGREE SURVEY (KIDS)
KiDS and VIKING together yield a unique wide survey with 9 bands coverage!
Can we exploit KiDS featuresto find out new lenses?
Can we exploit KiDS featuresto find out new lenses?
SDSS KiDS
Dieleman et al. (2015)Huertas-Company et al. (2015b)
Hoyle (2015)
NETWORK ARCHITECTURE?
