Strong Gravitational Lensing and ML: generative models for galaxies - - PowerPoint PPT Presentation

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Strong Gravitational Lensing and ML: generative models for galaxies - - PowerPoint PPT Presentation

Mar 06, 2023 162 likes •673 views

Strong Gravitational Lensing and ML: generative models for galaxies Adam Coogan Dark Machines workshop ICTP , 8-12 April 2019 Observed galaxy p ( src | x ) Generative model p ( lens | x ) Bayesian inference p ( sub | x ) Model

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SLIDE 1

Strong Gravitational Lensing and ML: generative models for galaxies

Adam Coogan

Dark Machines workshop ICTP , 8-12 April 2019

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SLIDE 2

Observed galaxy

p(θsrc|x) p(θlens|x) p(θsub|x)

Generative model

Model physics when possible, use machine learning for the rest

Bayesian inference

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SLIDE 3

Observed galaxy

http://great3.jb.man.ac.uk/

p(θsrc|x) p(θlens|x) p(θsub|x)

Generative model Bayesian inference

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SLIDE 4

Observed galaxy

Machine learning for generatively modeling the source light

http://great3.jb.man.ac.uk/

p(θsrc|x) p(θlens|x) p(θsub|x)

Generative model Bayesian inference

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SLIDE 5

Observed galaxy

Machine learning for generatively modeling the source light

  • Galaxies have diverse, complex morphologies (especially z≳2)

http://great3.jb.man.ac.uk/

p(θsrc|x) p(θlens|x) p(θsub|x)

Generative model Bayesian inference

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SLIDE 6

Observed galaxy

Machine learning for generatively modeling the source light

  • Galaxies have diverse, complex morphologies (especially z≳2)
  • Complex source → more accurate lens parameter inference

http://great3.jb.man.ac.uk/

p(θsrc|x) p(θlens|x) p(θsub|x)

Generative model Bayesian inference

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SLIDE 7

Observed galaxy

Machine learning for generatively modeling the source light

  • Galaxies have diverse, complex morphologies (especially z≳2)
  • Complex source → more accurate lens parameter inference

http://great3.jb.man.ac.uk/

p(θsrc|x) p(θlens|x) p(θsub|x)

Generative model Bayesian inference

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SLIDE 8

Observed galaxy

Machine learning for generatively modeling the source light

  • Galaxies have diverse, complex morphologies (especially z≳2)
  • Complex source → more accurate lens parameter inference

http://great3.jb.man.ac.uk/

p(θsrc|x) p(θlens|x) p(θsub|x)

Generative model Bayesian inference

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SLIDE 9

Source model

  • Low-dimensional representation of data that:

➡ Captures range of galaxy morphologies ➡ Has a latent space compatible with Bayesian inference

Kingma & Welling 2013, Rezende et al 2014

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SLIDE 10

Source model

  • Low-dimensional representation of data that:

➡ Captures range of galaxy morphologies ➡ Has a latent space compatible with Bayesian inference

Latent space z

x

Data

Kingma & Welling 2013, Rezende et al 2014

Variational autoencoder

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SLIDE 11

Source model

  • Low-dimensional representation of data that:

➡ Captures range of galaxy morphologies ➡ Has a latent space compatible with Bayesian inference

Latent space z

x

Data

Kingma & Welling 2013, Rezende et al 2014

Variational autoencoder

qϕ(z|x)

Encoder

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SLIDE 12

Source model

  • Low-dimensional representation of data that:

➡ Captures range of galaxy morphologies ➡ Has a latent space compatible with Bayesian inference

Latent space z

x

Data

Kingma & Welling 2013, Rezende et al 2014

Variational autoencoder

qϕ(z|x)

Encoder

pθ(x|z)

Decoder

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SLIDE 13

Source model

  • Low-dimensional representation of data that:

➡ Captures range of galaxy morphologies ➡ Has a latent space compatible with Bayesian inference

Latent space z

x

Data

p(z) = N(0, I)

Kingma & Welling 2013, Rezende et al 2014

Variational autoencoder

qϕ(z|x)

Encoder

pθ(x|z)

Decoder

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SLIDE 14

Source model

  • Low-dimensional representation of data that:

➡ Captures range of galaxy morphologies ➡ Has a latent space compatible with Bayesian inference

Latent space z

x

Data

p(z) = N(0, I)

Kingma & Welling 2013, Rezende et al 2014

Variational autoencoder

qϕ(z|x)

Encoder

pθ(x|z)

Decoder

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SLIDE 15

Source model

  • Low-dimensional representation of data that:

➡ Captures range of galaxy morphologies ➡ Has a latent space compatible with Bayesian inference

Latent space z

x

Data

p(z) = N(0, I)

Kingma & Welling 2013, Rezende et al 2014

Train encoder, decoder by maximizing lower bound on p(data)

Variational autoencoder

qϕ(z|x)

Encoder

pθ(x|z)

Decoder

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SLIDE 16

Galaxy VAE

  • Dataset: ~56,000 galaxies, redshifts ~ 1

http://great3.jb.man.ac.uk/

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SLIDE 17

Galaxy VAE

  • Dataset: ~56,000 galaxies, redshifts ~ 1

S/N < 10 S/N ~ 20 S/N > 100

http://great3.jb.man.ac.uk/

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SLIDE 18

Galaxy VAE

  • Dataset: ~56,000 galaxies, redshifts ~ 1

S/N < 10 S/N ~ 20 S/N > 100

This talk: train on ~10,000 images with S/N = 15 - 50

http://great3.jb.man.ac.uk/

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SLIDE 19
  • Encoder, decoder: deep convolutional neural networks

Galaxy VAE

  • Dataset: ~56,000 galaxies, redshifts ~ 1

Radford et al 2015 (DCGAN)

S/N < 10 S/N ~ 20 S/N > 100

This talk: train on ~10,000 images with S/N = 15 - 50 Eg, decoder:

http://great3.jb.man.ac.uk/

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SLIDE 20

Galaxy VAE: reconstructions

x

z ∼ qϕ(z|x)

x′

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SLIDE 21

Galaxy VAE: reconstructions

Original Reconstruction Original Reconstruction Original Reconstruction

x

z ∼ qϕ(z|x)

x′

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SLIDE 22

Galaxy VAE: reconstructions

Original Reconstruction Original Reconstruction Original Reconstruction

x

z ∼ qϕ(z|x)

x′

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SLIDE 23

Galaxy VAE: reconstructions

Original Reconstruction Original Reconstruction Original Reconstruction

x

z ∼ qϕ(z|x)

x′

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SLIDE 24

Galaxy VAE: reconstructions

Original Reconstruction Original Reconstruction Original Reconstruction

1. 2. 1. 2.

x

z ∼ qϕ(z|x)

x′

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SLIDE 25

Galaxy VAE: reconstructions

Original Reconstruction Original Reconstruction Original Reconstruction

1. 2. 1. 2.

x

z ∼ qϕ(z|x)

x′

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SLIDE 26

Galaxy VAE: reconstructions

Original Reconstruction Original Reconstruction Original Reconstruction

1. 2. 1. 2.

Rezende & Viola 2018, Zhao et al 2017

x

z ∼ qϕ(z|x)

x′

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SLIDE 27

Galaxy VAE: samples

z ∼ p(z) = N(0, I)

Hoffman & Johnson 2016, Alemi et al 2018

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SLIDE 28

Galaxy VAE: samples

z ∼ p(z) = N(0, I)

Hoffman & Johnson 2016, Alemi et al 2018

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SLIDE 29

Galaxy VAE: samples

z ∼ p(z) = N(0, I)

Hoffman & Johnson 2016, Alemi et al 2018

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SLIDE 30

Galaxy VAE: samples

z ∼ p(z) = N(0, I)

z distribution for training data

Hoffman & Johnson 2016, Alemi et al 2018

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SLIDE 31

Galaxy VAE: samples

z ∼ p(z) = N(0, I)

z distribution for training data

Hoffman & Johnson 2016, Alemi et al 2018

≠ N(0, I) →open issue with VAEs!

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SLIDE 32

Galaxy VAE: samples

z ∼ p(z) = N(0, I)

Our approach: sample z from here to generate better galaxies z distribution for training data

Hoffman & Johnson 2016, Alemi et al 2018

≠ N(0, I) →open issue with VAEs!

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SLIDE 33

Normalizing flows

z ∼ N(0, I) z′ ∼

Rezende & Mohamed 2015, Kingma et al 2016, …

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SLIDE 34

Normalizing flows

  • Compose invertible transformations with simple

Jacobians to reshape distributions

z ∼ N(0, I) z′ ∼

fT ∘ . . . ∘ f2 ∘ f1(z)

Rezende & Mohamed 2015, Kingma et al 2016, …

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SLIDE 35

Normalizing flows

  • Compose invertible transformations with simple

Jacobians to reshape distributions

  • Parametrize with neural networks

z ∼ N(0, I) z′ ∼

fT ∘ . . . ∘ f2 ∘ f1(z)

Rezende & Mohamed 2015, Kingma et al 2016, …

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SLIDE 36

Normalizing flows

  • Compose invertible transformations with simple

Jacobians to reshape distributions

  • Parametrize with neural networks
  • For our purposes: inverse autoregressive flows (IAFs),

which enable efficient sampling of the latent variable

z ∼ N(0, I) z′ ∼

fT ∘ . . . ∘ f2 ∘ f1(z)

Rezende & Mohamed 2015, Kingma et al 2016, …

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SLIDE 37

Galaxy VAE: samples

z distribution for training data z samples from IAF fit

x

z ∼ IAF(z)

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SLIDE 38

Galaxy VAE: samples

Generated galaxies z distribution for training data z samples from IAF fit

x

z ∼ IAF(z)

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SLIDE 39

Lensing galaxies

True source Observation

*Very preliminary, simplified analysis

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SLIDE 40

Lensing galaxies

True source Observation

*Very preliminary, simplified analysis

Best-fit source

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SLIDE 41

Lensing galaxies

True source Observation

True Einstein radius: 2.3 Best-fit value: 2.29 *Very preliminary, simplified analysis

Best-fit source

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SLIDE 42

Conclusions

  • Integrate galaxy VAE with full analysis pipeline
  • Improve prior/latent distribution mismatch:
  • Fully incorporate flows with VAE
  • Fix blurriness:
  • More flexible encoder? β/conditional-VAE, …?
  • Example of “differentiable programming” for physics + ML

Tomczak & Welling 2018 Higgins et al 2017

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SLIDE 43

Conclusions

  • Integrate galaxy VAE with full analysis pipeline
  • Improve prior/latent distribution mismatch:
  • Fully incorporate flows with VAE
  • Fix blurriness:
  • More flexible encoder? β/conditional-VAE, …?
  • Example of “differentiable programming” for physics + ML

Tomczak & Welling 2018 Higgins et al 2017

Thanks!

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SLIDE 44

Lensing MNIST digits

True source

Simplified lens with one parameter, rein Poissonian

  • bservation

noise

Observation

Outputs from simplified analysis

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SLIDE 45

Lensing MNIST digits

True source

Simplified lens with one parameter, rein Poissonian

  • bservation

noise

Observation Best-fit source from VAE

Outputs from simplified analysis

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SLIDE 46

Lensing MNIST digits

True source

Simplified lens with one parameter, rein Poissonian

  • bservation

noise

Observation Best-fit source from VAE

1.63 1.64 1.65 1.66 1.67 rein 20 40 60 80 100 p(rein|obs)

True rein HMC SVI

Lens parameter inference

Outputs from simplified analysis

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SLIDE 47

Training VAEs

  • Maximize a lower bound on :

ELBO(x(i)) = 𝔽e(z|x(i)) [log d(x(i)|z)] − KL [e(z|x(i))||m(z)]

Encoded means for MNIST

p(x(i))

Source

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SLIDE 48

Training VAEs

  • Maximize a lower bound on :

ELBO(x(i)) = 𝔽e(z|x(i)) [log d(x(i)|z)] − KL [e(z|x(i))||m(z)]

Encoded means for MNIST

p(x(i))

Source

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SLIDE 49

Training VAEs

  • Maximize a lower bound on :

ELBO(x(i)) = 𝔽e(z|x(i)) [log d(x(i)|z)] − KL [e(z|x(i))||m(z)]

Encoded means for MNIST

p(x(i))

Source

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SLIDE 50

Training VAEs

  • Maximize a lower bound on :

ELBO(x(i)) = 𝔽e(z|x(i)) [log d(x(i)|z)] − KL [e(z|x(i))||m(z)]

Encoded means for MNIST

p(x(i))

Source