Carol Cuesta-Lazaro (IAIFI Fellow)

in collaboration with Siddarth Mishra-Sharma and Tess Smidt

 Diffusion Models for Cosmology

Bridging simulations and observations of the Universe

Initial Conditions of the Universe

Laws of gravity

3-D distribution of galaxies

Which are the ICs of OUR Universe?

What is the origin of these fluctuations?

Probe Inflation

Galaxy formation

3-D distribution of dark matter

Is GR modified on large scales?

How do galaxies form?

ML for Large Scale Structure:

A 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

p(
)
|
\mathrm{Cosmology}
z_T
z_{0}
z_{1}
z_{2}
p_\theta(z_{t-1}|z_t)
q(z_t|z_{t-1})

Reverse diffusion: Denoise previous step

Forward diffusion: Add Gaussian noise (fixed)

Diffusion models

A person half Yoda half Gandalf

z_T
z_{0}
z_{1}

Diffusion on 6D coordinates

z_{2}
p_\theta(z_{t-1}|z_t)
q(z_t|z_{t-1})

Reverse diffusion: Denoise previous step

Forward diffusion: Add Gaussian noise (fixed)

Cosmology

Tractable likelihood!

p(x|\mathrm{cosmology})

Setting tight constraints with only 5000 galaxies

 

All learnable functions

Equivariant functions

Data constraints

Credit: Adapted from Tess Smidt

Equivariant diffusion

Implications for robustness and interpretability?

+ Galaxy formation

+ Observational systematics (Cut-sky, Fiber collisions)

Forward Model

N-body simulations

Observations

https://arxiv.org/pdf/1611.08606.pdf

Is the model robust to systematic errors?

 

How are simulations and data different?

 

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By carol cuesta

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