The Flow has not summarised this story yet — read it at arXiv Machine Learning.
arXiv:2610.16645v1 Announce Type: cross Abstract: Recovering divergence-free velocity fields from sparse and corrupted observations requires reconciling physical consistency, expressive representatio...
arXiv:2608. 04222v1 Announce Type: cross Abstract: Turbulence is a central testbed for machine learning on physical dynamics because its governing laws are known exactly.
arXiv:2507. 00719v3 Announce Type: replace-cross Abstract: Typically, numerical simulations of Earth systems are coarse, and Earth observations are sparse and gappy.
The paper introduces a local and sparse kernel method for learning solution operators of incompressible flows, replacing global output reconstruction with local divergence‑free interpolants and a multiscale kernel that approaches Kolmogorov statistics under refinement. A compactly supported, positive‑semidefinite kernel yields sparse operator regression, with support radius fitted to data and optional affine polynomials capturing global trends. The method employs Operator Lagrange weights to avoid forming local coefficients, achieving accuracy comparable to or better than previous dense methods and neural operators, while offering significant GPU speed‑ups and reduced storage.
arXiv:2604. 23874v3 Announce Type: replace-cross Abstract: The differentiable physics paradigm may be leveraged as an a-posteriori approach for discovering turbulence closure models by embedding a neural network parameterization directly inside the solver and optimizing it given potentially sparse target data.
arXiv:2601. 11440v3 Announce Type: replace-cross Abstract: Urban wind flow reconstruction is essential for assessing air quality, heat dispersion, and pedestrian comfort, yet remains challenging when only sparse sensor data are available.