Differentiable Cosmological Simulation with Adjoint Method

TL;DR

This paper introduces a novel differentiable cosmological simulation method using the adjoint approach, enabling larger, more accurate models and improved optimization without the memory constraints of traditional AD techniques.

Contribution

The authors develop an adjoint-based differentiable simulation framework for cosmology, overcoming memory limitations of existing methods and enhancing accuracy and scalability.

Findings

Enables larger, more precise cosmological simulations

Reduces memory usage compared to traditional AD methods

Improves gradient-based optimization and inference in cosmology

Abstract

Rapid advances in deep learning have brought not only myriad powerful neural networks, but also breakthroughs that benefit established scientific research. In particular, automatic differentiation (AD) tools and computational accelerators like GPUs have facilitated forward modeling of the Universe with differentiable simulations. Based on analytic or automatic backpropagation, current differentiable cosmological simulations are limited by memory, and thus are subject to a trade-off between time and space/mass resolution, usually sacrificing both. We present a new approach free of such constraints, using the adjoint method and reverse time integration. It enables larger and more accurate forward modeling at the field level, and will improve gradient based optimization and inference. We implement it in an open-source particle-mesh (PM) $N$-body library pmwd (particle-mesh with derivatives). Based on the powerful AD system JAX, pmwd is fully differentiable, and is highly performant on GPUs.