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.
arXiv:2507. 00719v3 Announce Type: replace-cross Abstract: Typically, numerical simulations of Earth systems are coarse, and Earth observations are sparse and gappy.
arXiv:2610.35123v1 Announce Type: cross Abstract: Generative AI offers new approaches to turbulence problems in which incomplete observations or unresolved d.o.f. admit multiple physically plausible...
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: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:2610.16645v1 Announce Type: cross Abstract: Recovering divergence-free velocity fields from sparse and corrupted observations requires reconciling physical consistency, expressive representatio...
arXiv:2608. 16546v1 Announce Type: cross Abstract: Most super-resolution models learn from paired data by supervising only the final high-resolution output.
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...
arXiv:2512. 19311v2 Announce Type: replace-cross Abstract: This paper studies the training-testing discrepancy (a.
arXiv:2606. 27354v1 Announce Type: cross Abstract: Neural surrogate models offer fast approximate mappings from PDE parameters to solutions, but they typically treat solving as a purely statistical task: once trained, they struggle to correct their own constraint violations and extrapolate beyond the training distribution.
arXiv:2608. 14744v1 Announce Type: new Abstract: Recovering high-resolution states from sparse, low-resolution observations is a central challenge in scientific machine learning and data assimilation.
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.
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.