  We present the first neural network that has learned to compactly represent
and can efficiently reconstruct the statistical dependencies between the values
of physical variables at different spatial locations in large 3D simulation
ensembles. Going beyond linear dependencies, we consider mutual information as
a measure of non-linear dependence. We demonstrate learning and reconstruction
with a large weather forecast ensemble comprising 1000 members, each storing
multiple physical variables at a 250 x 352 x 20 simulation grid. By
circumventing compute-intensive statistical estimators at runtime, we
demonstrate significantly reduced memory and computation requirements for
reconstructing the major dependence structures. This enables embedding the
estimator into a GPU-accelerated direct volume renderer and interactively
visualizing all mutual dependencies for a selected domain point.
