SELECTION OF STRONG GRAVITATIONAL LENSES WITH...
Transcript of SELECTION OF STRONG GRAVITATIONAL LENSES WITH...
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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
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STRONG GRAVITATIONAL LENSING
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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.
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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)
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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
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EXPECTED NUMBER OF LENSES
Now KiDS EUCLID
~700 ~1500 ~105
From simple lensing statistics.See, e.g., Pawase et al. 2012.
KIDS
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HOW TO FIND THEM?
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HOW TO FIND THEM?
• VISUAL INSPECTION
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HOW TO FIND THEM?
• VISUAL INSPECTION
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HOW TO FIND THEM?
• VISUAL INSPECTION
• AUTOMATED METHODS
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HOW TO FIND THEM?
• VISUAL INSPECTION
• AUTOMATED METHODS
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HOW TO FIND THEM?
• VISUAL INSPECTION
• AUTOMATED METHODS
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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.
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http://www.tensorflow.orgGoogle’s library for
Machine Intelligence.
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WHAT ARE NEURAL NETWORKS?
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Linear
Non-Linear
Data Parameters:Weights and biases
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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)
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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.
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From http://playground.tensorflow.org/
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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!
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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!
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CONVOLUTIONAL NETWORKS
Pooling layers:
• Down-sample the feature maps. • Reduce the number of the free parameters.• Create a sort of translational invariance.
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CONVOLUTIONAL NETWORKS
Pooling layers:
• Down-sample the feature maps. • Reduce the number of the free parameters.• Create a sort of translational invariance.
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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.
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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.
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MOCK DATA PRODUCTION
20 arcsec
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AFTER TRAINING ON 5 × 106 EXAMPLES
Some first layer filters learned by the network. They are actually searching for particular patterns.
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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.
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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.
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Visual inspection is still needed
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Visual inspection is still needed
But we need fewer monkeys!
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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.
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• 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)
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KiDS and VIKING together yield a unique wide survey with 9 bands coverage!
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Can we exploit KiDS featuresto find out new lenses?
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Can we exploit KiDS featuresto find out new lenses?
SDSS KiDS
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Dieleman et al. (2015)Huertas-Company et al. (2015b)
Hoyle (2015)
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NETWORK ARCHITECTURE?