Learning Incompressible 3D Flows from Sparse Samples: A Set Transformer Approach to Divergence-Free Kernel Fitting
Read the original on arXiv AI →The Flow has not summarised this story yet — read it at arXiv AI.
The Flow has not summarised this story yet — read it at arXiv AI.
The paper presents a turbulence‑aware framework for reconstructing high‑fidelity three‑dimensional flow fields from coarse‑grained data. It combines a multiscale neural operator with a state‑space model to enforce temporal consistency, incorporates Navier‑Stokes residuals as soft constraints, and uses a mixture‑of‑experts mechanism for unsupervised adaptation to unknown coarse‑graining. Experiments on canonical turbulent systems and atmospheric reanalysis data show reduced reconstruction errors and better preservation of multiscale spatial structure and coherent temporal evolution compared to existing learning‑based and classical baselines.
High-fidelity three-dimensional turbulent flow fields are crucial for scientific and engineering analyses, but direct numerical simulation or high-resolution measurements are costly. The paper introduces a turbulence-aware framework that couples a multiscale neural operator with a state space model and incorporates Navier-Stokes residuals as soft constraints to reconstruct time-resolved 3‑D flow fields from coarse-grained data. The method also uses a mixture-of-experts mechanism for unsupervised adaptation to unknown coarse-graining, and demonstrates reduced reconstruction errors and improved preservation of multiscale spatial structure and coherent temporal evolution on canonical turbulent systems and atmospheric reanalysis data.
The paper introduces Flow Divergence Sampler (FDS), a training‑free method that refines intermediate states in flow‑matching models by using the divergence of the marginal velocity field to detect and correct misguidance toward low‑density regions. FDS operates during inference, requires no additional training, and can be applied as a plug‑and‑play module with standard solvers and existing flow backbones. Experiments show that FDS consistently improves fidelity in tasks such as text‑to‑image synthesis and inverse problems.
The paper presents a Deep Operator Network that reconstructs full‑field 4D mitral regurgitation hemodynamics from sparse planar velocity data and boundary pressure traces. The network is pretrained on a URANS database of eleven orifice phantoms and then fine‑tuned on new cases, achieving rapid predictions in minutes. While the adaptation improves flow topology in the observed plane, reconstruction error increases sharply with distance from that plane, limiting physical consistency in the surrounding volume.
The paper introduces a kernel‑based operator learning method that preserves key physical properties—such as incompressibility, periodicity, and turbulence—of the incompressible Navier–Stokes equations. By mapping input functions to expansion coefficients in a property‑preserving kernel basis, the method guarantees that predicted velocity fields analytically maintain these properties. The authors provide theoretical convergence guarantees, develop efficient computational techniques for large‑scale training, and demonstrate significant accuracy and speed improvements over neural operators on 2D and 3D flow benchmarks.
arXiv:2610.07033v1 Announce Type: new Abstract: Predicting transient urban winds is fundamental to understanding urban microclimates and designing climate-resilient cities. Building-resolving large-e...