Cosmology's Midlife Crisis

IAIFI Fellow, MIT

Carolina Cuesta-Lazaro

Art: "A Bar at the Folies-Bergère" by Édouard Manet

Embracing the Machine Learning Makeover

\Lambda \mathrm{CDM}
["DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations" arXiv:2404.03002]

What role did Machine Learning play?

Dark Energy is constant over time

DESI's Dark Energy constraints

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

1-Dimensional

Machine Learning

Secondary anisotropies

Galaxy formation

Intrinsic alignments

DESI, DESI-II, Spec-S5

Euclid / LSST

Simons Observatory

CMB-S4

Ligo

Einstein

The era of Big Data Cosmology

xAstrophysics

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

5-Dimensional

w_0, w_a, f\sigma_8, \Omega_m, \sum m_\nu

Dataset Size = 1 

Can't poke it in the lab 

Simulations

Bayesian statistics

Cosmology is hard

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

smsharma/awesome-neural-sbi

Astrophysics dominates Simulation-based Inference

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

Unicorn land The promise of ML for Cosmology

Reality Check Roadblocks & Bottlenecks

Outline of this talk

Mapping dark matter

Reverting gravitational evolution

Field Level Inference

Learning to represent baryonic feedback

Data-driven hybrid simulators

Unsupervised problems

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

Inference a la gradient descent

Base Distribution

Target Distribution

Bridging two distributions

z \sim p(z)
p(z)
x \sim p(x)
p(x)
\mathcal{L}_\phi = -\sum_i \log p_\phi(x_i)

Make the data as likely as possible

Prompt

A person half Yoda, half Gandalf

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

[Image Credit: Claire Lamman (CfA/Harvard) / DESI Collaboration]

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

["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

Long range correlations

Huge pointclouds (20M)

Homogeneity and isotropy

Siddharth Mishra-Sharma

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

Fixed Initial Conditions / Varying Cosmology

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

p(\theta|x) = \frac{p(x|\theta)p(\theta)}{p(x)}

Diffusion model

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

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]

 

Nayantara Mudur

["Your diffusion model is secretly a certifiably robust classifier" 
Chen et al

arXiv:2402.02316]

CNN

Diffusion

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p_\phi(\rho_\mathrm{DM}|\rho_\mathrm{Galaxies})

1 to Many:

Distribution of Galaxies

Underlying Dark Matter 

["Debiasing with Diffusion: Probabilistic reconstruction of Dark Matter fields from galaxies" 
Ono et al (including Cuesta-Lazaro) arXiv:2403.10648]

 

Victoria Ono

Core Park

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Truth

Sampled

Observed

Small

Large

Scale (k)

Power Spectrum

Small

Large

Scale (k)

Cross correlation

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

TNG-300

True DM

Sample DM

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

["3D Reconstruction of Dark Matter Fields with Diffusion Models: Towards Application to Galaxy Surveys" 
Park, Mudur, Cuesta-Lazaro et al (in-prep)]

 

Posterior Sample

Posterior Mean

Debiasing Cosmic Flows

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

Reconstructing dark matter back in time

Stochastic Interpolants

NF

p(\delta_\mathrm{ICs}, \theta|\delta_\mathrm{Obs}) =
p(\delta_\mathrm{ICs}|\delta_\mathrm{Obs})
p(\theta|\delta_\mathrm{ICs},\delta_\mathrm{Obs})

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

p(x_1|x_0)
x_0

?

x_1
s
["Probabilistic Forecasting with Stochastic Interpolants and Foellmer Processes" 
Chen et al arXiv:2403.10648 (Figure adapted from arXiv:2407.21097)]

 

Generative SDE

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

\mathcal{L} = \int_0^1 \mathbb{E} | \hat{b}_s(X_s, x_0) - b_s(X_s, x_0)| ^2 ds
(x_0, x_1) \sim p(x_0,x_1)
b_s(x, x_0) = \mathbb{E} \left[\dot{I}_s \right]
x_1 \sim p(x_1|x_0)
I_s = \alpha_s x_0 + \beta_s x_1 + \sigma_s W_s

Stochastic Interpolant

Boundary Conditions

\alpha_0 = \beta_1 = 1
\alpha_1 = \beta_0 = \sigma_1 = 0

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

Simulating what you need (and sometimes what you want)

Guided simulations with fuzzy constraints

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

Simulating what you need

(and sometimes what you want)

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

How do we learn what is the robust information?

Simulating dark matter is easy!

"Atoms" are hard" :(

N-body Simulations

Hydrodynamics

Can we improve our simulators in a data-driven way?

How well can we simulate the Universe?

(if cold!)

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

 ~ Gpc

pc

kpc

Mpc

Gpc

[Video credit: Francisco Villaescusa-Navarro]

Gas density

Gas temperature

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

Small

Large

\langle\mathrm{True}\,\,\mathrm{Pred}\rangle

In-Distribution

In-Distribution

In-Distribution

Out-of-Distribution

Out-of-Distribution

Out-of-Distribution

Out-of-Distribution

Out-of-Distribution

Out-of-Distribution

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

["Multifield Cosmology with Artificial Intelligence" 
Villaescusa-Navarro et al arXiv:2109.09747]


Out-of-Distribution

In-Distribution

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

Mikhail Ivanov

Robust galaxy bias model: Effective field Theories 

+ Simulation as priors

p(b)
p(\mathrm{Galaxies}|b)

Field-level EFT

["Full-shape analysis with simulation-based priors: constraints on single field inflation from BOSS" 
Ivanov, Cuesta-Lazaro et al arXiv:2402.13310]

 

Andrej Obuljen

Michael Toomey

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

["Full-shape analysis with simulation-based priors: cosmological parameters and the structure growth anomaly" 
Ivanov, Obuljen, Cuesta-Lazaro, Toomey arXiv:2409.10609]

 

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

Representation Learning

Informative abstractions of the data

Transfer learning beyond LCDM

Cosmic web Anomaly Detection

Representing baryonic feedback

What makes a good representation?

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

General

Predictive

Low dimensional?

Should generalize across scales, systems...

Transfer to unseen conditions

p(x|z)

Simple : Occam's razor

Causal?

Representation Learning a la gradient descent

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

Contrastive

Generative

inductive biases

from scratch or from partial observations

Students at MIT are

OVER-CAFFEINATED

NERDS

SMART

ATHLETIC

\Omega_m, \sigma_8

Simulator 1

Simulator 2

z
p(
, z)

Dark Matter

Feedback

\Omega_m, \sigma_8

i) Contrastive

Learning the feedback manifold

Baryonic fields

ii) Generative

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

Baryonic fields

Dark Matter

Generative model

Total matter, gas temperature,

gas metalicity

p(
)
, z)
p(
z = f_\theta (
)

Encoder

+

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

p(\mathcal{C},z|
)
z

What is the space of plausible solutions and how do we search it?

Differentiable Galaxies ODEs

Our best bet

\frac{d \mathrm{Galaxies}}{dt} = \phi(\mathrm{Dark Matter}(t))
+ \phi_\theta(?)

Neural Network corrections

Finding the missing pieces

Data-driven hybrid simulators

Are these models predictive?

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

Parity violation cannot be originated by gravity

7 \sigma
x
\mathrm{Mirror}(x)
["Measurements of parity-odd modes in the large-scale 4-point function of SDSS..." 
Hou, Slepian, Chan arXiv:2206.03625]
?
1 \sigma
["Could sample variance be responsible for the parity-violating signal seen in the BOSS galaxy survey?"
 Philcox, Ereza arXiv:2401.09523]

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

x
\mathrm{Mirror}(x)
\mathrm{max} \, \left( f_\theta(x) - f_\theta(\mathrm{Mirror}(x)) \right)

Real or Fake?

x or Mirror x?

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

Train

Test

Me: I can't wait to work with observations

Me working with observations:

Very subtle effect -> Hard to find data efficient architectures

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024

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 limits the amount of information we can robustly extract

Hybrid simulators, forward models, robustness

Unsupervised problems

 

Mapping dark matter, constrained simulations... Let's get creative!

Field level inference

Conclusions

Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024