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.
By Ramansh Sharma, Matthew Lowery, Houman Owhadi, Varun Shankar
arXiv:2610.16645v1 Announce Type: cross
Abstract: Recovering divergence-free velocity fields from sparse and corrupted observations requires reconciling physical consistency, expressive representatio...
By Ramzi Idoughi, Radouan Boukharfane, Peter Wonka
arXiv:2611.06912v1 Announce Type: cross
Abstract: Reconstructing full flow fields from sparse sensors requires prior assumptions about unmeasured regions and physical variables. Yet it remains unclea...
By Nicolas Tricard, Linzheng Wang, Jason Chen, Sili Deng
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.
By Yilong Dai, Yiming Sun, Yiheng Chen, Shengyu Chen, Peyman Givi, Xiaowei Jia, Runlong Yu
RheOPT is a transformer-based neural operator that first pretrains on inexpensive Newtonian fluid simulations and then fine‑tunes on a small set of non‑Newtonian samples. By reusing geometry‑conditioned transport structures rather than the Newtonian constitutive response, RheOPT achieves accurate few‑shot predictions for complex fluids such as Giesekus, Oldroyd‑B, and Bingham in a contraction channel and for oscillatory wake flows behind a triangular obstacle. The approach demonstrates that Newtonian pretraining can match or surpass models trained from scratch with four times as many non‑Newtonian samples, especially when using reversible instance normalization.
By Maedeh Saberi, Amir Barati Farimani, Safa Jamali
The paper introduces iFLEX, a model that refines simple numerical interpolation for temporal gaps in scientific data. It first creates a weighted average of two observations, then trains a conditional diffusion model to generate the residual between this estimate and the true intermediate field. Experiments on turbulence, radar precipitation, and sea surface temperature show that iFLEX reduces reconstruction error compared to optical‑flow and other diffusion baselines.
By Pu Ren, Michael W. Mahoney, N. Benjamin Erichson