Generative Models in Astrophysics

Carol Cuesta-Lazaro

IAIFI Fellow

Initial Conditions of the Universe

Laws of gravity

3-D distribution of galaxies

Which are the ICs of OUR Universe?

Primordial non-Gaussianity?

Probe Inflation

Galaxy formation

3-D distribution of dark matter

Is GR modified on large scales?

How do galaxies form?

Neutrino mass hierarchy?

Dall-e 3

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Emulate complex processes in high dimensions

x \sim p(x|y)

y = \{ \Omega_{cdm}, \sigma_8, ... \}

arXiv:2206.04594

Generative AI for physics

Super resolution

arxiv:2010.06608

Generative AI for physics

Compare data and simulations optimally

Simulation-based Inference

arXiv:1911.01429

Generative AI for physics

Detect anomalies

arxiv:2010.14554

Generative AI for physics

Model uncertainties

arxiv:2010.14554

Current Universe

Initial Conditions

Generative AI for physics

Represent complex priors

arxiv:2206.14820

how does a galaxy look like?

lensing

Generative AI for physics

p_\phi(x)

Data

A parametric PDF

Maximise the likelihood

(or something similar)

Generative AI for physics

2. Sample

x \sim p_\phi(x)

1. Estimate densities

p_\phi(x)

Explicit Density

Implicit Density

Tractable Density

Approximate Density

Normalising flows

Variational Autoencoders

Diffusion models

Generative Adversarial Networks

The zoo of generative models

The backbone of vision generative models

Reverse diffusion: Denoise previous step

Forward diffusion: Add Gaussian noise (fixed)

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Diffusion Models

z_T

z_{0}

z_{1}

Diffusion on point clouds

z_{2}

q_\theta(z_{t-1}|z_t)

p(z_t|z_{t-1})

Reverse diffusion: Denoise previous step

Forward diffusion: Add Gaussian noise (fixed)

Cosmology

"Diffusion generative modeling for galaxy surveys: emulating clustering for inference at the field level" Carolina Cuesta-Lazaro, Siddarth Mishra-Sharma

Generating galaxy point clouds for redshift surveys

Setting tight constraints with only 5000 halo positions

p(x,y,z, v_x, v_y, v_z, M_h|\Omega_m, \sigma_8)

Halo Mass Function

Velocity

PDF

Mean pairwise velocity

(Probabilistic) reconstruction of Dark Matter

"Probabilistic Reconstruction of Dark Matter fields from galaxies using diffusion models"
Victoria Ono, Core Francisco Park,  Nayantara Mudur, Yueying Ni, Carolina Cuesta-Lazaro (in prep)

p_\phi(x_\mathrm{DM}|x_\mathrm{Stars})

(Probabilistic) reconstruction of Dark Matter

(Probabilistic) reconstruction of Dark Matter

"Probabilistic Reconstruction of Dark Matter fields from galaxies using diffusion models"
Victoria Ono, Core Francisco Park,  Nayantara Mudur, Yueying Ni, Carolina Cuesta-Lazaro (in prep)

Differentiable PM Simulators

h_0

h_1

h_5

h_4

h_2

h_3

h_6

Node features coordinates (+mass, velocities)

Input

Noisy halo properties

Output

Noise prediction

Graph Neural Networks as score models

kNN (~20)