Forecasting the power of higher order weak-lensing statistics with automatically differentiable simulations

Aims. We present the fully differentiable physical Differentiable Lensing Lightcone (DLL) model, designed for use as a forward model in Bayesian inference algorithms that require access to derivatives of lensing observables with respect to cosmological parameters. Methods. We extended the public FlowPM N -body code, a particle-mesh N -body solver, while simulating the lensing lightcones and implementing the Born approximation in the Tensorflow framework. Furthermore, DLL is aimed at achieving high accuracy with low computational costs. As such, it integrates a novel hybrid physical-neural (HPN) parameterization that is able to compensate for the small-scale approximations resulting from particle-mesh schemes for cosmological N -body simulations. We validated our simulations in the context of the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST) against high-resolution κ TNG-Dark simulations by comparing both the lensing angular power spectrum and multiscale peak counts. We demonstrated its ability to recover lensing C ℓ up to a 10% accuracy at ℓ = 1000 for sources at a redshift of 1, with as few as ∼0.6 particles per Mpc h −1 . As a first-use case, we applied this tool to an investigation of the relative constraining power of the angular power spectrum and peak counts statistic in an LSST setting. Such comparisons are typically very costly as they require a large number of simulations and do not scale appropriately with an increasing number of cosmological parameters. As opposed to forecasts based on finite differences, these statistics can be analytically differentiated with respect to cosmology or any systematics included in the simulations at the same computational cost of the forward simulation. Results. We find that the peak counts outperform the power spectrum in terms of the cold dark matter parameter, Ω c , as well as on the amplitude of density fluctuations, σ 8 , and the amplitude of the intrinsic alignment signal, A IA .