← 研踪 PaperTrailarXiv:2603.24500 · v2
Project and Generate: Divergence-Free Neural Operators for Incompressible Flows
首次提交 2026-03-26 00:40
版本更新 2026-11-07 00:53
雷达观测 2026-11-09 13:22
摘要
Learning-based models for fluid dynamics often operate in unconstrained function spaces, leading to physically inadmissible, unstable simulations. Penalty-based methods can reduce constraint violations but do not guarantee exact incompressibility. In this work, we introduce a unified framework that enforces the incompressible continuity equation as a hard, intrinsic constraint for both deterministic and generative modeling. We integrate a differentiable spectral Leray projection into neural operators to enforce incompressibility. For flow matching, we construct a divergence-free Gaussian reference measure via a curl-based pushforward, so that the reference samples, interpolation paths, and velocity targets are compatible with the projected dynamics. Experiments on 2D Navier-Stokes equations demonstrate exact incompressibility up to discretization error and substantially improved stability and physical consistency.
观测到的版本
相邻记录可能跳过中间版本；首次发现 v2 及以上也会标为版本更新。
v2 · 2026-11-07 00:53 · 最新观测版本
Project and Generate: Divergence-Free Neural Operators for Incompressible Flows
Learning-based models for fluid dynamics often operate in unconstrained function spaces, leading to physically inadmissible, unstable simulations. Penalty-based methods can reduce constraint violations but do not guarantee exact incompressibility. In this work, we introduce a unified framework that enforces the incompressible continuity equation as a hard, intrinsic constraint for both deterministic and generative modeling. We integrate a differentiable spectral Leray projection into neural operators to enforce incompressibility. For flow matching, we construct a divergence-free Gaussian reference measure via a curl-based pushforward, so that the reference samples, interpolation paths, and velocity targets are compatible with the projected dynamics. Experiments on 2D Navier-Stokes equations demonstrate exact incompressibility up to discretization error and substantially improved stability and physical consistency.
查看此版本解读 →查看此版本原文 ↗