  We present a GPU-accelerated numerical approach for fast kernel and
differential background solutions. The model image proposed in the Bramich
(2008) difference image analysis algorithm is analogous to a very simple
Convolutional Neural Network (CNN), with a single convolutional filter (i.e.
the kernel) and an added scalar bias (i.e. the differential background). Here,
we do not solve for the discrete pixel array in the classical, analytical
linear least-squares sense. Instead, by making use of PyTorch tensors (GPU
compatible multi-dimensional matrices) and associated deep learning tools, we
solve for the kernel via an inherently massively parallel optimisation. By
casting the Difference Image Analysis (DIA) problem as a GPU-accelerated
optimisation which utilises automatic differentiation tools, our algorithm is
both flexible to the choice of scalar objective function, and can perform DIA
on astronomical data sets at least an order of magnitude faster than its
classical analogue. More generally, we demonstrate that tools developed for
machine learning can be used to address generic data analysis and modelling
problems.
