  We apply physics-informed neural networks (PINNs) to first-order two-scale
periodic asymptotic homogenization of the property tensor in a generic elliptic
equation. The problem of lack of differentiability of property tensors at the
sharp phase interfaces is circumvented by making use of diffuse interface
formulation. Periodic boundary conditions are incorporated strictly, through
the introduction of an input-transfer layer (Fourier feature mapping), in which
the sine and cosine of the inner product of position vectors and reciprocal
lattice vectors are considered. This, together with the absence of Dirichlet
boundary conditions, results in a lossless boundary condition application. The
only loss terms are then due to the differential equation itself, which removes
the necessity of scaling the loss entries. In demonstrating the formulation's
versatility based on the reciprocal lattice vectors, crystalline arrangements
defined with Bravais lattices are used. We also show that considering integer
multiples of the reciprocal basis in the Fourier mapping leads to improved
convergence of high-frequency functions. We consider applications in one, two,
and three dimensions. Periodic composites, composed of embeddings of
monodisperse inclusions in the form of disks/spheres in the
two-/three-dimensional matrix, are considered. For demonstration purposes,
stochastic monodisperse disk arrangements are also considered.
