Problem
Research questions and friction points this paper is trying to address.
incompressible flow
density transport
velocity field
transport trajectory
optimization
A Variational Optimal Transport Operator on Incompressible Flow
🤖 AI Summary
本文提出了一种变分不可压缩最优传输算子VIOT，通过生成散度自由的速度场来快速解决不可压缩密度传输问题，相比传统方法大幅提高了计算速度。
📝 Abstract
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 Operator backbone that amortizes the solve across new pairs and grid resolutions. Together, these components make incompressible transport a reusable neural operator that facilitates various transport processes. Further, the generative capability extends beyond the training distribution, with VIOT producing incompressible transports for user-drawn source-target pairs in a real-time interactive system. We demonstrate VIOT on 2D and 3D density-transport benchmarks. Both 2D and 3D rollouts complete in seconds per pair, while per-instance baselines in our 2D comparisons optimize each new pair from scratch and require on the order of an hour, a roughly $10^4\times$ online speedup.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Variational Incompressible Optimal Transport
divergence-free velocity field
Fourier Neural Operator
amortized incompressible density transport
real-time interactive system
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