  Piecewise Linear Interface Construction (PLIC) is frequently used to
geometrically reconstruct fluid interfaces in Computational Fluid Dynamics
(CFD) modeling of two-phase flows. PLIC reconstructs interfaces from a scalar
field that represents the volume fraction of each phase in each computational
cell. Given the volume fraction and interface normal, the location of a linear
interface is uniquely defined. For a cubic computational cell (3D), the
position of the planar interface is determined by intersecting the cube with a
plane, such that the volume of the resulting truncated polyhedron cell is equal
to the volume fraction. Yet it is geometrically complex to find the exact
position of the plane, and it involves calculations that can be a computational
bottleneck of many CFD models. However, while the forward problem of 3D PLIC is
challenging, the inverse problem, of finding the volume of the truncated
polyhedron cell given a defined plane, is simple. In this work, we propose a
deep learning model for the solution to the forward problem of PLIC by only
making use of its inverse problem. The proposed model is up to several orders
of magnitude faster than traditional schemes, which significantly reduces the
computational bottleneck of PLIC in CFD simulations.
