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
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
Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024
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
Carolina Cuesta-Lazaro IAIFI/MIT @ AI goes MAD 2024
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
AIGoesMAD24
By carol cuesta
