  Vacuum fluctuations of quantum fields between physical objects depend on the
shapes, positions, and internal composition of the latter. For objects of
arbitrary shapes, even made from idealized materials, the calculation of the
associated zero-point (Casimir) energy is an analytically intractable
challenge. We propose a new numerical approach to this problem based on
machine-learning techniques and illustrate the effectiveness of the method in a
(2+1) dimensional scalar field theory. The Casimir energy is first calculated
numerically using a Monte-Carlo algorithm for a set of the Dirichlet boundaries
of various shapes. Then, a neural network is trained to compute this energy
given the Dirichlet domain, treating the latter as black-and-white pixelated
images. We show that after the learning phase, the neural network is able to
quickly predict the Casimir energy for new boundaries of general shapes with
reasonable accuracy.
