  The formation of the large-scale structure, the evolution and distribution of
galaxies, quasars, and dark matter on cosmological scales, requires numerical
simulations. Differentiable simulations provide gradients of the cosmological
parameters, that can accelerate the extraction of physical information from
statistical analyses of observational data. The deep learning revolution has
brought not only myriad powerful neural networks, but also breakthroughs
including automatic differentiation (AD) tools and computational accelerators
like GPUs, facilitating forward modeling of the Universe with differentiable
simulations. Because AD needs to save the whole forward evolution history to
backpropagate gradients, current differentiable cosmological simulations are
limited by memory. Using the adjoint method, with reverse time integration to
reconstruct the evolution history, we develop a differentiable cosmological
particle-mesh (PM) simulation library pmwd (particle-mesh with derivatives)
with a low memory cost. Based on the powerful AD library JAX, pmwd is fully
differentiable, and is highly performant on GPUs.
