Deep learning domain translation <br> between mock observations and hydrodynamical simulations

Deep learning domain translation
between mock observations and hydrodynamical simulations

08/09/2023

Link/QR code to the slides for later or to follow along

deep learning: skepticism in scientific community
why bother with deep learning models?
generalisation and knowledge compression
- mathematical equations, e.g. \[ R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R = 8 \pi T_{\mu\nu} \]
"hyper"-parametrized models

Credit: J. Capehart (2022)

deep neural networks are generally black-box models
still, can be supplemented with explainability techniques
- identifying data or model weaknesses
- verify results
- optimize model performance
SHAP (Lundberg and Lee 2017), LIME (Ribeiro et al. 2016),
saliency maps (Simonyan et al. 2013), etc.

find parameters \(\theta\) to approximate a true data density
\[ P_\theta(x) \sim P_\text{data}(x) \]
condition the generative process with additional information \(c\): \[ P_\theta(x|c) \sim P_\text{data}(x|c) \]
- image-to-image translation

Figure 1: Credit: Jun-Yan Zhu

GANs (pix2pix, CycleGAN, SRGAN, …): \(\quad \mathbb{E}_{x\sim p_\text{data}}[\log{D_\theta(x)}] + \mathbb{E}_{z\sim q(z)}[1-\log{D_\theta(G_\theta(z))}]\)
- fast, high quality, implicit density, mode collapse
Diffusion Models (see Mariia's talk): \(\quad -\log{p(x)} \le \mathbb{E}_{q}[\log{\frac{q(x_{1:T}\vert x_0)}{p_\theta(x_{0:T})}}]\)
- flexible, high fidelity, lower bound to LL, slow inference
VAEs: \(\quad \log{p(x)} \ge \mathbb{E}_{z\sim q_{\theta}(z\vert x)}[\log{p_\theta(x\vert z)}] - D_{KL}\left(q_\theta(z\vert x) \vert\vert p(z)\right)\)
- fast, regularized latent space, lower bound to LL, trade-offs: reconstruction ⇿ regularization
Normalizing flows: \(\quad p_{\theta}(x) = p(f_{\theta}(x)) \cdot J_{f_{\theta}^{-1}}(x)\)
- invertible, latent variable, exact likelihood, expensive in high-dimensional spaces

compress the knowledge from hydrodynamical and mock simulations to
- map properties from simulations to mock observations
- infer (hidden) astrophysical properties from observables
computational:
- explore the usability of various deep learning techniques
  for scientific data

cosmological & astrophysical processes from first principle
latest simulations reach (almost) petabyte sizes ⇾ ideal for deep learning
- IllustrisTNG, Simba, FIRE, EAGLE, Phoebos, and others
- CAMELS btw.

learn the mapping from domain A ⇿ B
domain A: gas
domain B: HI brightness temperature \[T_b(\mathbf{x}) = 189 h \frac{H_0}{a^2H(a)} \frac{\rho_{\text{HI}}(\mathbf{x})}{\rho_c}\,\text{mK}\] see Villaescusa-Navarro et al. (2018)