"The Galaxy–Halo Connection and Differentiable Modeling with JAX"

Summary:

Understanding how galaxies form and evolve within dark matter halos, the so-called galaxy–haloconnection, is a central problem in modern astrophysics. Over the past two decades, increasingly precise observations have revealed tight statistical relationships between galaxy properties and the assembly histories of their host halos. At the same time, next-generation surveys demand models that are not only physically interpretable, but also computationally scalable and statistically robust.

In this pedagogical talk, I will begin with an introductory overview to the galaxy–halo connection:

what it is, why it matters for galaxy formation and cosmology, and how it underpins forward-modeling approaches that connect theoretical predictions to observed galaxy populations. I will briefly outline the specific problem I am working on, constructing differentiable, physically motivated models that connect halo growth to galaxy star formation histories, and explain how this framework enables applications ranging from large-scale structure analyses to Bayesian inference of individual galaxy properties.

The second half of the talk will shift toward methodology, with an introduction to JAX, the high-performance numerical computing library that enables these models. Using a Jupyter notebook, I will demonstrate key features of JAX, including automatic differentiation, vectorization, just-in-time compilation, and GPU acceleration, and show how these tools make it possible to build fast, differentiable forward models. The goal of this part is to provide both conceptual understanding and practical insight into how modern differentiable programming techniques can be applied to problems in galaxy formation and cosmology.