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
The paper presents a lightweight retraining strategy for a parameterized Reduced Order Model (ROM) that achieves full‑model accuracy using only a fraction of the computational effort and sparse observations. The ROM architecture combines a Variational Autoencoder for dimensionality reduction with a transformer network that evolves latent states while accounting for the Reynolds number as an external control variable. By leveraging the probabilistic VAE, the method generates trajectory ensembles and uncertainty estimates, and adapts to out‑of‑sample parameters through sparse data assimilation with an ensemble Kalman filter, focusing retraining on the autoencoder to correct latent manifold distortions.
By Isma\"el Zighed, Andrea N\'ovoa, Luca Magri, Taraneh Sayadi
arXiv:2602.23188v2 Announce Type: replace
Abstract: We propose an efficient retraining strategy for a parameterized Reduced Order Model (ROM) that attains accuracy comparable to full retraining while...
By Isma\"el Zighed, Andrea N\'ovoa, Luca Magri, Taraneh Sayadi
arXiv:2609.38049v1 Announce Type: new
Abstract: Generative models for function-valued data, such as time series and solutions of partial differential equations, must learn distributions over infinite...
By Fred Xu, Thomas Markovich, Barbora Barancikova, Yizhou Sun
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.
By Ashwin Suriyanarayanan, Dibyajyoti Chakraborty, Romit Maulik
Generative models for function-valued data, such as time series and solutions of partial differential equations, must learn distributions over infinite-dimensional spaces. Functional Flow Matching (FF...
arXiv:2601. 20496v2 Announce Type: replace-cross Abstract: Generating dense physical fields from sparse measurements is a fundamental question in sampling, signal processing, and many other applications.
By Ofek Aloni, Barak Fishbain