arXiv AI By Pu Ren, Michael W. Mahoney, N. Benjamin Erichson

Generative Refinement Learning for Temporal Interpolation in Scientific Machine Learning

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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.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

arXiv Machine Learning
Oct 22

Local and Sparse Kernel Operator Learning for Incompressible Flows: An Operator Lagrange Formulation

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.

By Ramansh Sharma, Matthew Lowery, Houman Owhadi, Varun Shankar