MLizing cosmology

florpi

The What? How? And Why?

And really, Why?

https://florpi.github.io/

IAIFI Fellow

Carol Cuesta-Lazaro

The Why: The limits of analytical models

But... Access to tones of data!

simulated data

Complex non-Gaussian distributions

Non-linear forward models

(Image Credit: D. Schlegel/Berkeley Lab using data from DESI)

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

ML has solved high-dimensional inference

#1 Field-level likelihoods for galaxy surveys

Siddharth Mishra-Sharma

#2 Probabilistic reconstruction of the cosmic web

Core Park

Nayantara Mudur

Victoria Ono

Yueying Ni

#3 Faster, invertible and more accurate simulators

Sarah Jeffreson

Chirag Modi

Generative Models 101

p(x)

x_1

x_2

PDF

Samples

Parametric PDF

Maximize the likelihood of the training samples

\hat \theta = \argmax \left[ \log p_\theta (x_\mathrm{train}) \right]

p_\theta(x)

Reverse diffusion: Denoise previous step

Forward diffusion: Add Gaussian noise (fixed)

A person half Yoda half Gandalf

q_\theta(z_0|z_1)

p(z_1|z_0)

Diffusion generative models

p(z_0)

p(z_T)

p(z_2)

p(z_1)

p(z_2|z_1)

p(z_T|z_2)

q_\theta(z_1|z_2)

q_\theta(z_2|z_T)

s_\theta(x,t) = \nabla_x \log p_t(x)

Score

#1 Modelling galaxy surveys

"A point cloud approach to generative modeling for galaxy surveys at the field level" 
arXiv:2311.17141
Carolina Cuesta-Lazaro and Siddharth Mishra-Sharma

2PCF

Mean pairwise

velocity

kNN

Emulating cosmic variance

2PCF

kNN

Diffusion models approximate the likelihood

\log p(z_0) = \log \int p(z_{0:T}) dz_{1:T} \approx

\approx \sum_{i=1}^T \mathbb{E}_{q(z_{i}|z_0)} D_{KL} \left[p(z_i | z_{i-1}, z_0) || q_\theta(z_{i-1} | z_{i}) \right]

arxiv:2107.00630

arxiv:2208.11970

Maximum Likelihood = Denoising

Tight constraints with only 5000 positions!

 "Probabilistic Reconstruction of Dark Matter fields from galaxies using diffusion models"
arXiv:2311.08558
Core Francisco Park,  Victoria Ono, Nayantara Mudur, Yueying Ni, Carolina Cuesta-Lazaro

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

#2 Solving inverse problems:

Probabilistic reconstruction of the cosmic web

1 to Many:

25 \, h^{-1}\mathrm{Mpc}

#3 AI Powered simulators

Fast and differentiable N-body sims

Inverting dynamics

More accurate hydro sims: Resolving star formation rates

z=120

z=0.2

~10-100 pc

Molecular clouds

where stars form

Hydro sims:

A matrioska of scales

~10-50 kpc

Galaxies

where clouds form

TNG50 ~50 Mpc

Cosmic web

(where galaxies form)

Adapted from: "Learning the learning the Universe" by Jake Bennet

MXXL ~ 4 Gpc

Current subgrid models of the ISM

High Res Sim

Springel and Hernquist 03

Learning subgrid models from high resolution isolated galaxies

Gas Surface Density

SFR Surface Density

Hybrid simulators

Nbody

Slow

Non-differentiable

Particle mesh

Accurate

Fast

Differentiable

Missing small scales

Nbodyify

Fast

Differentiable

Accurate

 "Nbodyify: adaptive mesh corrections for PM simulations"
Carolina Cuesta-Lazaro and Chirag Modi (in prep)

\frac{\mathrm{d} \mathbf{x}}{\mathrm{d} a } = \frac{1}{a^3 E(a)}\mathbf{v}

\frac{\mathrm{d} \mathbf{v}}{\mathrm{d} a } = \frac{1}{a^2 E(a)}\mathbf{F}(\mathbf{x},a)

\mathbf{F}_\theta(\mathbf{x},a) = \frac{3 \Omega_m}{2} \nabla \left[\phi^\mathrm{PM}(\mathbf{x}) + \phi^\mathrm{corr}_\theta(\mathbf{x}, a, \phi^\mathrm{PM}, \delta^\mathrm{PM}) \right]

\mathbf{F}(\mathbf{x},a) = \frac{3 \Omega_m}{2} \nabla \phi^\mathrm{PM}(\mathbf{x})

Gravitational evolution ODE

Particle-mesh

Hybrid Simulator

#2 Probabilistic reconstruction of the cosmic web

#1 Field-level likelihoods for galaxy surveys

#3 Faster, invertible and more accurate simulators

cuestalz@mit.edu