A Variational Optimal Transport Operator on Incompressible Flow
We present the Variational Incompressible Optimal Transport (VIOT) operator, a generative neural operator for amortized incompressible density transport. Given a new source-target density pair, VIOT predicts a divergence-free velocity field and generates the full transport trajectory by feed-forward inference, replacing the hour-scale per-pair optimization used by adjoint fluid solvers and differentiable simulation baselines. The system consists of three components: a stream-function or vector-potential representation that enforces incompressibility by construction, a regularized incompressible transport objective that balances endpoint accuracy and flow smoothness, and a Fourier Neural O...
| Authors | Jinjin He, Shenyifan Lu, Sinan Wang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 12 September 2026 |
| Last updated at source | 12 September 2026 |
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