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. While penalty-based methods offer soft regularization, they provide no structural guarantees, resulting in spurious divergence and long-term collapse. 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. First, to project deterministic models onto the divergence-free subspace, we integrate a differentiable spectral Leray projection grounded in the Helmholtz-Hodge decomposition, which restricts the regression hypothesis ...
| Authors | Xigui Li, Hongwei Zhang, Ruoxi Jiang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 25 March 2026 |
| Last updated at source | 25 March 2026 |
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