Data-driven galaxy morphology models for image simulations

Francois Lanusse

with Rachel Mandelbaum

Blending Task Force Meeting

7 Jan. 2019

A few words about  Generative Models

Variational Auto-Encoder

  • Trained to reproduce the input image while trying to match the latent representation to a given prior
\log p(x) \geq E_{z \sim q_{\varphi}(. | x)}[\log p_{\bm{\theta}}(x | z)] - \mathbb{D}_{KL}[q_{\varphi}(\bm{z} | x) || p(z)]

Balance between code regularization and image quality

Input

Reconstruction

Input

Reconstruction

\log p(x) \geq E_{z \sim q_{\varphi}(. | x)}[\log p_{\bm{\theta}}(x | z)] - \mathbb{D}_{KL}[q_{\varphi}(\bm{z} | x) || p(z)]

Low KL divergence

High KL divergence

Illustration from Engel et al. 2018

Conditional Masked Autoregressive Flows for sampling from VAE

  • MAF is a state-of-the-art ML technique for density estimation using neural network
  • We train a VAE with high KL divergence (i.e. low reconstruction loss) and use a MAF to model the effective distribution of the latent space
     
  • Using a conditional MAF, we can adjust the  distribution in the latent space to correspond to populations with desired properties

flux_radius [normalised]

code distribution
for real images

code distribution
learned by MAF

Training a Generative Model on COSMOS galaxies

  • We use the GalSim COSMOS 25.2 sample as our training set
     
  • We include the PSF as part of the generative model
    • Last layer of the model is a convolution by the  known PSF
    • Generative model will output essentially unconvolved images
       
  • We use a proper log likelihood taking into account the noise correlations
     
  • We first train an unconditional VAE (time consuming) and then train on top of it a conditional MAF sampler (relatively fast)
    • Our fiducial model is conditioned on size and magnitude

Some examples 

Parametric

MAF-VAE

COSMOS

AutoEncoder Reconstruction

Residuals

Second order moments

Morphological

statistics 

M and D statistics from  Freeman et al. 2014

The GalSim Interface

Packaging and serving models

  • We want a generic interface that can be used to execute any user provided trained generative model
     
  • Tensorflow Hub Library:
    • Computational Graph and trained Weights packaged in single .tar.gz archive
    • Takes a set of named inputs, returns a tensor 
    • Package additional meta-information (e.g. pixel size, stamp size)
       
  • Created galsim-hub, a repository of trained deep generative models which can directly be used by installing the galsim-hub GalSim extension:

 

$ pip install --user galsim-hub
import galsim
import galsim_hub
from astropy.table import Table

model = galsim_hub.GenerativeGalaxyModel('hub:cosmos_size_mag')

# Defines the input conditions
cat = Table([[5., 10. ,20.], 
             [24., 24., 24.]],
             names=['flux_radius', 'mag_auto'])

# Sample light profiles for these parameters
ims = model.sample(cat)

# Convolve by PSF
ims = [galsim.Convolve(im, psf) for im in ims]

modules:
    - galsim_hub

psf :
    type : Gaussian
    sigma : 0.06  # arcsec

gal :
    type : GenerativeModelGalaxy
    flux_radius : { type : Random , min : 5, max : 10 }
    mag_auto : { type : Random , min : 24., max : 25. }

image :
    type : Tiled
    nx_tiles : 10
    ny_tiles : 10
    stamp_size : 64  # pixels
    pixel_scale : 0.03  # arcsec / pixel
    noise :
       type : COSMOS

output :
    dir : output_yaml
    file_name : demo14.fits

input :
    generative_model :
        file_name : 'hub:cosmos_size_mag'

Python Interface

Yaml driver

$ galsim demo.yaml

Interfacing with BlendingToolKit

  • BTK uses the WeakLensingDeblending package to draw images
     
  • Weak Lensing Deblending represents galaxies a sums of Sersic profiles (bulge + disk) and potentially AGN
     
  • bulge + disk parameters, flux in each band is provided by extragalactic catalog
     
  • How can we interface with the generative model in this setting?

Blending ToolKit

COSMOS parametric fits

  • The COSMOS  sample provided with GalSim includes bulge+disk parametric fits for a subset of galaxies
     
  • We can use these  parameters to condition the generative model:
    • zphot, bulge_hlr, disk_hlr, bulge_q, disk_q, bulge_flux, disk_flux
       
  • The image is drawn for the i-band, and flux is rescaled to match the input catalog in each band

Similar scheme would allow us to draw galaxies image for DC2/DC3

Example of running scarlet on

parametric vs generative model

  • Blends drawn and processed through Scarlet using Sowmya's tools.
     
  • In most cases results are very similar, but some visible residuals for more extended objects.
     
  • Working on more quantitative results.

Parametric:

Generative model:

Conclusion

  • Framework for integrating generative models with GalSim
     
  • Will release  models based on COSMOS along with code to train your own models (GAN and VAE)
     
  • These  generative models will allow us to include more realistic morphologies for galaxies in future image simulations
     
  • Update of Ravanbakhsh et al. 2017