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The formation of the large-scale structure, the evolution and distribution ofgalaxies, quasars, and dark matter on cosmological scales, requires numericalsimulations. Differentiable simulations provide gradients of the cosmologicalparameters, that can accelerate the extraction of physical information fromstatistical analyses of observational data. The deep learning revolution hasbrought not only myriad powerful neural networks, but also breakthroughsincluding automatic differentiation (AD) tools and computational acceleratorslike GPUs, facilitating forward modeling of the Universe with differentiablesimulations. Because AD needs to save the whole forward evolution history tobackpropagate gradients, current differentiable cosmological simulations arelimited by memory. Using the adjoint method, with reverse time integration toreconstruct the evolution history, we develop a differentiable cosmologicalparticle-mesh (PM) simulation library pmwd (particle-mesh with derivatives)with a low memory cost. Based on the powerful AD library JAX, pmwd is fullydifferentiable, and is highly performant on GPUs.

pmwd: A Differentiable Cosmological Particle-Mesh $N$-body Library