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?
deck
By carol cuesta
