Neural bases improve reduced models for simulating fluid flows
Neural Eigenfluid Bases: Spectral Objectives, Gauge, and Topology
Machine Learning
Summary
Simulating fluid flow can be complicated and slow because it involves many details. The authors introduce Neural Eigenfluid Bases, a technique that uses neural networks to represent the main patterns of fluid movement with fewer components. This approach keeps important physical rules like incompressibility and handles obstacles well. Their method achieves high accuracy with much smaller data, allowing fast and efficient fluid simulations.
What this means in practice
- •For computational engineers: Create fast and accurate reduced-order fluid simulations that maintain physical constraints for design and analysis tasks.
- •For video game developers: Integrate efficient fluid dynamics approximations for real-time visual effects without sacrificing realistic flow behavior.$Commercial implications: Enables selling games or simulation software with high-quality fluid visuals and interactions that run smoothly on consumer hardware.
Authors
Baiming Zhang, Shiying Xiong, Zhecheng Wang
Abstract
Reduced-order models simplify fluid simulation by representing complex flows with a small number of spatial modes. Building on Laplacian Eigenfluids, we introduce Neural Eigenfluid Bases (NEB), a neural representation whose basis functions can be evaluated anywhere in space. We enforce incompressibility and impermeable boundaries directly through differential lifts and potential boundary conditions. Geometry-local orthogonalization and Rayleigh minimization then learn an ordered basis. We connect learning in potential and velocity spaces, and derive a spectral-variance relation explaining why these objectives weight approximate modes differently, even though their exact positive spectra agree. Gauge fixing reduces the number of spatial derivatives needed for potential learning, while a Dirichlet energy loss learns independent circulation fields around obstacles. With 1024 modes, both objectives keep velocity errors below 1% in periodic vortex merger. For random flows around obstacles, potential-based learning captures more initial energy and gives lower final errors than numerical Laplacian bases of the same size. The reduced state is about a thousand times smaller than the full reference model. Three-dimensional tests separate spatial reconstruction errors from errors in coefficient evolution. Precomputed Galerkin operators allow millisecond-scale updates when the same basis is reused across simulations. This provides a physically constrained basis for continuous flow reconstruction and efficient reduced-order simulation.