A Variational Optimal Transport Operator on Incompressible Flow

This paper presents the Variational Incompressible Optimal Transport (VIOT) operator, a generative neural operator designed for amortized incompressible density transport. VIOT predicts divergence-free velocity fields and generates complete transport trajectories through feed-forward inference, eliminating the per-pair optimization required by traditional adjoint fluid solvers. The system integrates three components to handle stream function or vector potential representations for incompressible flow applications.