DISCO-DJ performs large-scale structure (LSS) cosmological simulations with full support for automatic differentiation via the JAX (ascl:2111.002) ecosystem. It integrates a suite of modern cosmological modelling tools, including a fast particle-mesh (PM) N-body solver enhanced by theory-informed time integrators, such as BullFrog and FastPM (ascl:1905.010), and discreteness-suppression techniques (e.g., de-aliasing, sheet-based resampling, higher-order mass assignment kernels). The code also provides an interface to a differentiable Einstein–Boltzmann solver, high-order Lagrangian perturbation theory (nLPT) recursion relations, and semi-classical propagator perturbation theory (PPT). By utilizing JAX’s forward- and reverse-mode automatic differentiation (including memory-efficient adjoint methods), DISCO-DJ enables cosmological inference scenarios where differentiable pipelines from initial conditions to late-time observables are required.

The original MUSIC code (ascl:1311.011) was designed to provide initial conditions for zoom initial conditions and is limited for applications to large-scale cosmological simulations. MUSIC2-monofonIC generates high order LPT/PPT cosmological initial conditions for single resolution cosmological simulations, and can be used for rapid predictions of large-scale structure. MUSIC2-monofonIC offers support for up to 3rd order Lagrangian perturbation theory, PPT (Semiclassical PT for Eulerian grids) up to 2nd order, and for mixed CDM+baryon sims. It direct interfaces with CLASS and can use file input from CAMB; it offers multiple output modules for RAMSES (ascl:1011.007), Arepo (ascl:1909.010), Gadget-2/3 (ascl:0003.001), and HACC via plugins, and new modules/plugins can be easily added.

MUSIC generates multi-scale initial conditions with multiple levels of refinements for cosmological ‘zoom-in’ simulations. The code uses an adaptive convolution of Gaussian white noise with a real-space transfer function kernel together with an adaptive multi-grid Poisson solver to generate displacements and velocities following first- (1LPT) or second-order Lagrangian perturbation theory (2LPT). MUSIC achieves rms relative errors of the order of 10−4 for displacements and velocities in the refinement region and thus improves in terms of errors by about two orders of magnitude over previous approaches. In addition, errors are localized at coarse-fine boundaries and do not suffer from Fourier space-induced interference ringing.