Differentiable Cosmological Simulation with Adjoint Method

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.

5 figures + 2 tables; repo at https://github.com/eelregit/pmwd ; v2 matches published version with better typesetting

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• Large-scale dark matter simulations
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• Learning effective physical laws for generating cosmological hydrodynamics with Lagrangian Deep Learning
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• Differentiable Cosmological Hydrodynamics for Field-Level Inference and High Dimensional Parameter Constraints
• Learning the Universe: Learning to Optimize Cosmic Initial Conditions with Non-Differentiable Structure Formation Models
• Introducing cosmosTNG: simulating galaxy formation with constrained realizations of the COSMOS field
• Analytic auto-differentiable $\Lambda$CDM cosmography
• A Hamiltonian, post-Born, three-dimensional, on-the-fly ray tracing algorithm for gravitational lensing
• Differentiable Fuzzy Cosmic-Web for Field Level Inference