Carol Cuesta-Lazaro (IAIFI Fellow)
in collaboration with Siddarth Mishra-Sharma
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Generative models for the Large Scale Structure
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ML for Large Scale Structure:
Carol's wish list
Generative models
Learn p(x)
Evaluate the likelihood of a 3D map, as a function of the parameters of interest
1
Combine different galaxy properties (such as velocities and positions)
2
Sample 3D maps from the posterior distribution
3
![](https://newscenter.lbl.gov/wp-content/uploads/2022/01/allframe-1000mpc-960x540-1.gif)
Explicit Density
Implicit Density
Tractable Density
Approximate Density
Normalising flows
Variational Autoencoders
Diffusion models
Generative Adversarial Networks
The zoo of generative models
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/10464337/pasted-from-clipboard.png)
Reverse diffusion: Denoise previous step
Forward diffusion: Add Gaussian noise (fixed)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/10464337/pasted-from-clipboard.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/10464337/pasted-from-clipboard.png)
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Diffusion models
A person half Yoda half Gandalf
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/10245028/pasted-from-clipboard.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/10245033/pasted-from-clipboard.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/10245034/pasted-from-clipboard.png)
Diffusion on point clouds
Reverse diffusion: Denoise previous step
Forward diffusion: Add Gaussian noise (fixed)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/10245034/pasted-from-clipboard.png)
Cosmology
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/10459369/ezgif.com-resize.gif)
![](https://github.com/smsharma/set-diffuser/blob/main/notebooks/plots/animation_both_norotate.gif?raw=true)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/10459309/knn-2.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/10499434/velocity_summaries.png)
Halo Mass Function
Velocity
Mean pairwise velocity
Evidence Lower Bound
Distance to true posterior
Find
1. ELBO is a lower bound of the evidence
2. Maximising ELBO = Minimising KL
Maximise ELBO to maximise ev/likelihood
Maximise ELBO to approximate true posterior
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/10597125/pasted-from-clipboard.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/9947274/pasted-from-clipboard.png)
+ Galaxy formation
+ Observational systematics (Cut-sky, Fiber collisions)
+ Lightcone, Redshift Space Distortions....
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/9947316/pasted-from-clipboard.png)
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Forward Model
N-body simulations
Observations
Copy of Copy of Copy of deck
By carol cuesta
Copy of Copy of Copy of deck
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