arXiv Machine Learning By Weinan Wang, Bowen Gang, Hao Deng

Operator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regime

Read the original on arXiv Machine Learning →

arXiv:2606. 08654v1 Announce Type: new Abstract: In this paper, we propose a perturbation-based conformal prediction framework for uncertainty quantification in operator learning, with a focus on the 2D Navier--Stokes equations.

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 Machine Learning.

arXiv Machine Learning
Sep 14

Physics-Informed Conformal Prediction: Embedding PDE Consistency into Distribution-Free Uncertainty Quantification for Neural Operators

Physics-Informed Conformal Prediction (PI‑CP) embeds PDE residuals into the nonconformity score of split conformal prediction, yielding distribution‑free prediction intervals with provable coverage that adapt spatially to physics violations. The method demonstrates consistent 89‑91% coverage across six physics scenarios, outperforming MC Dropout and Deep Ensembles, while Fourier Neural Operators (FNO) achieve superior accuracy over CNN and DeepONet. Additionally, the authors prove that FNO’s translation equivariance limits its ability to solve PDEs with Dirichlet boundary conditions, and show that adding coordinate channels can reduce error by up to 63×.

By Michael Chin
arXiv Machine Learning
Jul 1

On Optimal Data Splitting for Split Conformal Prediction

arXiv:2606. 31600v1 Announce Type: cross Abstract: Conformal prediction and its variants, including the split conformal prediction, provide a distribution-free framework for uncertainty quantification by constructing prediction intervals or sets with finite-sample coverage guarantees.

By Sayan Das, Bahram Yaghooti, Todd A. Kuffner, Soumendra N. Lahiri