  We perform an exploratory study of a new approach for evaluating Feynman
integrals numerically. We apply the recently-proposed framework of
physics-informed deep learning to train neural networks to approximate the
solution to the differential equations satisfied by the Feynman integrals. This
approach relies neither on a canonical form of the differential equations,
which is often a bottleneck for the analytical techniques, nor on the
availability of a large dataset, and after training yields essentially
instantaneous evaluation times. We provide a proof-of-concept implementation
within the PyTorch framework, and apply it to a number of one- and two-loop
examples, achieving a mean magnitude of relative difference of around 1% at two
loops in the physical phase space with network training times on the order of
an hour on a laptop GPU.
