Carol Cuesta-Lazaro (IAIFI Fellow)
and Siddarth Mishra-Sharma (IAIFI Fellow)
Diffusion generative modelling for galaxy surveys
Initial Conditions of the Universe
Gaussian RF
Laws of gravity
3-D distribution of galaxies
Which are the ICs of OUR Universe?
Primordial non-Gaussianity?
3-D distribution of dark matter
Is GR modified on large scales?
How do galaxies form?
Neutrino mass hierarchy?
ML for the Large Scale Structure of the Universe:
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
p(
)
|
\mathrm{Interesting}
\mathrm{parameters}
z_T
z_{0}
z_{1}
z_{2}
p(z_t|z_{t-1})
Reverse diffusion: Denoise previous step
Forward diffusion: Add Gaussian noise (fixed)
Diffusion models
A person half Yoda half Gandalf
q_\theta(z_{t-1}|z_t)
q_\theta(z_{t-1}|z_t) = \mathcal{N}(z_{t-1}|\mu_\theta(z_t), \sigma_t)
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
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)
p(x,y,z, v_x, v_y, v_z, M_h|\Omega_m, \sigma_8)
Halo Mass Function
Velocity
Mean pairwise velocity
\mathcal{L}_T(x) = \sum_{i=1}^T \mathbb{E}_{q(z_{i}|x)} D_{KL} \left[q(z_{i-1} | z_{i}, x) || p_\theta(z_{i-1} | z_{i}) \right]
-\log p(x) \leq -\mathrm{VLB}(x)
D_{KL}(q(z_T|x) || p(z_T)) + \mathbb{E}_{q(z_0|x)} \left[-\log p(x|z_0) \right] + \mathcal{L}_T(x)
Prior loss
Diffusion loss
Reconstruction loss
Be a true Bayesian: Always maximise the likelihood
arxiv:2107.00630
arxiv:2303.00848
Maximum Likelihood = Denoising
Setting tight constraints with only 5000 halo positions
+ Galaxy formation
+ Observational systematics (Cut-sky, Fiber collisions)
+ Lightcone, Redshift Space Distortions....
Forward Model
N-body simulations
Observations
p(
)
|
\mathrm{Cosmology}
Optimise information on cosmological parameters
(robust) surprises
The challenge for field level inference
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By carol cuesta
