  We present MADLens a python package for producing non-Gaussian lensing
convergence maps at arbitrary source redshifts with unprecedented precision.
MADLens is designed to achieve high accuracy while keeping computational costs
as low as possible. A MADLens simulation with only $256^3$ particles produces
convergence maps whose power agree with theoretical lensing power spectra up to
$L{=}10000$ within the accuracy limits of HaloFit. This is made possible by a
combination of a highly parallelizable particle-mesh algorithm, a sub-evolution
scheme in the lensing projection, and a machine-learning inspired sharpening
step. Further, MADLens is fully differentiable with respect to the initial
conditions of the underlying particle-mesh simulations and a number of
cosmological parameters. These properties allow MADLens to be used as a forward
model in Bayesian inference algorithms that require optimization or
derivative-aided sampling. Another use case for MADLens is the production of
large, high resolution simulation sets as they are required for training novel
deep-learning-based lensing analysis tools. We make the MADLens package
publicly available under a Creative Commons License
(https://github.com/VMBoehm/MADLens).
