Big Data Cosmology meets AI
IAIFI Fellow
Carolina Cuesta-Lazaro
AstroAI Workshop - 20th June 2024
Video Credit: N-body simulation Francisco Villaescusa-Navarro
The era of Big Data Cosmology
1-Dimensional
Machine Learning
Secondary anisotropies
Galaxy formation
Intrinsic alignments
Dust
xAstrophysics
DESI, DESI-II, Spec-S5
Euclid
LSST
Simons Observatory
CMB-S4
Ligo
Einstein
LSST
Early Universe Inflation
{\delta_\mathrm{Initial}}
Late Universe
Energy and matter content
Evolution
{\delta_\mathrm{Final}}
\color{darkgray}{\Omega_m}
Dark matter
Dark energy
\color{darkgreen}{w_0, w_a}
\color{darkolive}{H_0}
Hubble Constant
\color{darkred}{\Omega_b}
\color{darkblue}{\sum m_\nu}
Baryons
Neutrino masses
\color{purple}{f_\mathrm{NL}}
\color{darkorange}{n_s}
Non-Gaussianity
Tilt power spectrum
Hubble tension
Beyond the Standard Model
Multifield Inflation
The Universe's forward model
Cosmological (field level) Inference for Galaxy Surveys
DESI
Point clouds and equivariance
Hybrid ML - Physics Simulators
Learning missing physics
Self-supervised representations
Anomaly detection / OOD
A forward model samples the likelihood
\theta
Parameters
Observable
x
DESI
Forward Model
\color{darkgray}{\Omega_m}, \color{darkgreen}{w_0, w_a},\color{purple}{f_\mathrm{NL}}\, ...
Dark matter
Dark energy
Inflation
p(x|\theta) = \int dz p(x,z|\theta)
A 2D animation of a folk music band composed of anthropomorphic autumn leaves, each playing traditional bluegrass instruments, amidst a rustic forest setting dappled with the soft light of a harvest moon
Image credit: DALL·E 3
1024x1024
p(x|\mathcal{C})?
p(x|\mathrm{prompt})
"A point cloud approach to generative modeling for galaxy surveys at the field level"
Cuesta-Lazaro and Mishra-Sharma
arXiv:2311.17141
Base Distribution
Target Distribution
- Sample
- Evaluate
Siddharth Mishra-Sharma
Fixed Initial Conditions
Varying Cosmology
Trained on only 5000 positions!
Nayantara Mudur
"Diffusion-HMC: Parameter Inference with Diffusion Model driven Hamiltonian Monte Carlo"
Mudur, Cuesta-Lazaro and Finkbeiner
in prep
p(\delta_m|\Omega_m, \sigma_8)
CNN
Diffusion
Increasing Noise
p(\sigma_8|\delta_m)
p(\sigma_8|\delta_m + 0.01 \epsilon)
p(\sigma_8|\delta_m + 0.02 \epsilon)
"Diffusion-HMC: Parameter Inference with Diffusion Model driven Hamiltonian Monte Carlo"
Mudur, Cuesta-Lazaro and Finkbeiner
p(x|\mathcal{C})
\mu_\theta(z_t,t)
p(z_T)
Making homogeneous and isotropic Universes
Base Distribution
Denoiser
=
p(
)
p(
p(
)
Invariant
Equivariant
=
p(
)
p(
=
p(
)
p(
All learnable functions
All learnable functions constrained by your data
All Equivariant functions
More data efficient!
Equivariant models
Non-equivariant
SEGNN: arXiv:2110.02905
NequIP: arXiv:2101.03164
p_\phi(\delta_\mathrm{z=127}|\delta_\mathrm{z=0})
1 to Many:
1 \mathrm{Gpc}/h
https://arxiv.org/abs/2210.02747https://arxiv.org/abs/2302.00482Stochastic Interpolants: Bridging arbitrary densities
"Stochastic Interpolants: A Unifying Framework for Flows and Diffusions"
Albergo, Boffi, Vanden-Eijnden
arXiv:2303.08797
x_1
x_0
\frac{d x_t}{dt} = u_t(x_t)
Flow ODE
x_0
p(x_0)
p(x_1)
x_1
u_t
\frac{d p_t}{dt} = - \left(\nabla u_t p_t \right)(x_t)
Continuity Equation
Regress the velocity field
L_\mathrm{FM} = \mathrm{min} \, \mathbb{E}_{t, p_t(x|x_0)} \left |\left| v^\theta_t(x|x_0) - u_t(x|x_0) \right|\right|^2
Unknown!
x_t = (1 - t) x_0 + t x_1
p_t(x|x_0)
p_0(x|x_0) = \delta_{x_0}
p_1(x|x_0) = p
Boundary Conditions
Conclusions
1. There is a lot of information in galaxy surveys that ML methods can access
2. We can tackle high dimensional inference problems so far unatainable
3. Our ability to simulate will limit the amount of information we can extract
Hybrid simulators, forward models, robustness, unsupervised problems
Dark matter density reconstruction, Initial Conditions, let's get creative!
Field level inference
cuestalz@mit.edu
Cross correlation
Final
<Reconstructed,True>
Scale (k)
Scale (k)
Small
Large
Small
Large
Initial
<Reconstructed,True>
Comparison to Hamiltonian Monte Carlo for Particle Mesh
d(32^3)
AstroAI Workshop2024
By carol cuesta
