Generative Solutions for Cosmic Problems

florpi

https://florpi.github.io/

IAIFI Fellow

Carol(ina) Cuesta-Lazaro

1. Observations x Simulations

2. Learning a general parametrisation for feedback

Outline

Constrained Simulations

(IC reconstruction)

3. Compressing simulation snapshots in continuous time

Inverse modelling

Data driven subgrid models

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

1. Reconstructing DM

TNG-300

True DM

Inferred DM

Size of training simulation

Galaxy Cluster

Void

 [arXiv:2403.10648]

Model trained on Astrid subgrid model

["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

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

p(\delta_\mathrm{ICs}|\delta_\mathrm{Obs})

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

2. Reconstructing DM back in time

3. Simulating what you need (and sometimes what you want)

Guided simulations with fuzzy constraints

4. Machine learned subgrid models

1. Predictive Simulators learned subgrid models from high resolution simulations

\frac{\partial \mathbf{u}}{\partial t} = \mathcal{H}[\mathbf{x},\mathbf{R}_{\theta}(\mathbf{x})]

Hydro simulator

Subgrid model

\mathrm{HR} : \mathrm{SFR}_{\theta}(\rho^\mathrm{LR}_\mathrm{gas},\rho^\mathrm{LR}_\mathrm{stars}, w^\mathrm{LR}_\mathrm{rot})

\frac{\partial \mathbf{u}}{\partial t} = \mathcal{H}_\mathrm{LR}[\mathbf{x}, \mathrm{SFR}_{\theta}(\rho^\mathrm{LR}_\mathrm{gas},\rho^\mathrm{LR}_\mathrm{stars}, w^\mathrm{LR}_\mathrm{rot}) )

Solution: train on the fly

\frac{\partial \mathcal{L}(\theta)}{\partial \theta} = \frac{\partial \mathcal{L}}{\partial \mathbf{u}} \cdot \frac{\partial \mathbf{u}}{\partial t} \cdot \frac{\partial \mathcal{H}[\mathbf{x}, \mathbf{R}_{\theta}(\mathbf{x})]}{\partial \theta}

\mathcal{L}(\theta) = \mathbb{E} \left[ \left\| \mathrm{SFR}_{\text{pred}}(\theta) - \mathrm{SFR}_{\text{HR}} \right\|^2 \right]

2. Data-driven subgrid models learned subgrid models from high dimensional observations

\frac{\partial \mathbf{u}}{\partial t} = \mathcal{H}[\mathbf{x},\mathbf{R}_{\theta}(\mathbf{x})]

Hydro simulator

Subgrid model

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

Are these models predictive?

4. Machine learned subgrid models

[Image credit: Sarah Jeffreson's beautiful high res sims]

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

Out-of-Distribution

In-Distribution

4. Learning the feedback manifold

Representation Learning

Informative abstractions of the data

Transfer learning beyond LCDM

Cosmic web Anomaly Detection

Representing baryonic feedback

Representation Learning a la gradient descent

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)

Dark Matter

Feedback

\Omega_m, \sigma_8

i) Contrastive

Baryonic fields

ii) Generative

Baryonic fields

Dark Matter

Generative model

Total matter, gas temperature,

gas metalicity

)

, z)

z = f_\theta (

)

Encoder

p(\mathcal{C},z|

)

5. Compressing simulations in continuous time

~ 10 trillion particles per snapshot stored

x Discrete snapshots

(x,y,z,t)

\Psi, \dot \Psi

x500