  The accurate numerical solution of partial differential equations is a
central task in numerical analysis allowing to model a wide range of natural
phenomena by employing specialized solvers depending on the scenario of
application. Here, we develop a variational approach for solving partial
differential equations governing the evolution of high dimensional probability
distributions. Our approach naturally works on the unbounded continuous domain
and encodes the full probability density function through its variational
parameters, which are adapted dynamically during the evolution to optimally
reflect the dynamics of the density. For the considered benchmark cases we
observe excellent agreement with numerical solutions as well as analytical
solutions in regimes inaccessible to traditional computational approaches.
