arXiv Machine Learning June 9, 2026 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.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.

benchmarks

arXiv AI

Jun 10

Conformal Prediction for Neural Operators: Distribution-Free Uncertainty Quantification in Physics Simulation

arXiv:2606. 09923v1 Announce Type: cross Abstract: Neural operators such as the Fourier Neural Operator (FNO) have emerged as powerful surrogates for solving partial differential equations (PDEs), achieving speedups of several orders of magnitude over traditional numerical solvers.

By Michael Chin

benchmarks safety

arXiv Machine Learning

Jun 30

Randomized neural operator for parametric PDEs with fast training and conformal uncertainty quantification

arXiv:2606. 29440v1 Announce Type: new Abstract: Repeatedly solving parametric PDEs is essential for uncertainty quantification, design optimization and inverse problems, but conventional neural operators require expensive non-convex training.

By Zirui Deng, Jingbo Sun, Deyu Meng, Fei Wang

benchmarks

arXiv Machine Learning

Jul 1

Accelerating Conformal Prediction via Approximate Leave-One-Out

arXiv:2606. 31915v1 Announce Type: cross Abstract: While conformal prediction provides a general framework for uncertainty quantification in predictive inference, its application is often limited by computational cost.

By Jiachen Cong, Jingbo Liu

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

arXiv Machine Learning

Aug 5

Conformal risk control for model-form uncertainty in parametric non-intrusive reduced-order models

arXiv:2608. 03360v1 Announce Type: cross Abstract: Non-intrusive reduced-order models (NIROMs) have become a standard tool for approximating parametric partial differential equations from computer design of experiments while significantly reducing computational costs.

By Edgar Jaber (CB, ENS Paris Saclay), R\'emy Vallot (CB, Michelin), Thibault Dairay (CB, Michelin), Mathilde Mougeot (CB, ENSIIE, ENS Paris Saclay)

benchmarks

arXiv Machine Learning

Jun 26

Uncertainty quantification via conformal prediction in data assimilation

arXiv:2606. 27001v1 Announce Type: new Abstract: Quantifying the evolution of uncertainty is critical to both probabilistic forecasting and data assimilation in numerical weather prediction.

By Catherine George, Alireza Javanmardi, Tijana Janji\'c, Eyke H\"ullermeier

Related stories

Conformal Prediction for Neural Operators: Distribution-Free Uncertainty Quantification in Physics Simulation

Randomized neural operator for parametric PDEs with fast training and conformal uncertainty quantification

Accelerating Conformal Prediction via Approximate Leave-One-Out

On Optimal Data Splitting for Split Conformal Prediction

Conformal risk control for model-form uncertainty in parametric non-intrusive reduced-order models

Uncertainty quantification via conformal prediction in data assimilation