  We use machine learning methods to approximate a classical density
functional. As a study case, we choose the model problem of a Lennard Jones
fluid in one dimension where there is no exact solution available and training
data sets must be obtained from simulations. After separating the excess free
energy functional into a "repulsive" and an "attractive" part, machine learning
finds a functional in weighted density form for the attractive part. The
density profile at a hard wall shows good agreement for thermodynamic
conditions beyond the training set conditions. This also holds for the equation
of state if it is evaluated near the training temperature. We discuss the
applicability to problems in higher dimensions.
