  Modeling of physical systems includes extensive use of software packages that
implement the accurate finite element method for solving differential equations
considered along with the appropriate initial and boundary conditions. When the
problem size becomes large, time needed to solve the resulting linear systems
may range from hours to weeks, and if the input parameters need to be adjusted,
even slightly, the simulations has to be re-done from scratch. Recent advances
in machine learning algorithms and their successful applications in various
fields demonstrate that, if properly chosen and trained, these models can
significantly improve conventional techniques. In this note we discuss
possibilities to complement the finite element studies with machine learning
and provide several basic examples.
