Enforces hard incompressibility constraints in neural operators using spectral Leray projection, ensuring physically admissible fluid simulations.
March 26, 2026
Original Paper
Project and Generate: Divergence-Free Neural Operators for Incompressible Flows
arXiv · 2603.24500
The Takeaway
Existing neural operators for fluids rely on soft penalty terms that often lead to spurious divergence and physical collapse. This framework guarantees exact incompressibility by construction, significantly improving the stability and reliability of AI-driven fluid dynamics for engineering applications.
From the abstract
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 dete