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: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
arXiv:2610.00535v1 Announce Type: new
Abstract: Uncertainty quantification is critical in scientific machine learning, where black-box, image-based models are increasingly deployed in high-stakes set...
By Carrie J. Lei-Cramer, Michael S. Jones, Laura J. Wendelberger
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
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: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: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)
The paper introduces a tail‑aware geometry learning framework for multivariate conformal prediction using ellipsoids. It decouples tail sensitivity from coverage guarantees by learning a metric matrix through volume minimization under a CVaR constraint, followed by standard conformal calibration. The approach is convex, prioritizes high‑residual samples, and theoretically balances ellipsoidal volume against tail severity, with experiments confirming its effectiveness.
By Xiang Zhang
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
arXiv:2507. 20975v5 Announce Type: replace-cross Abstract: Operator models are regression algorithms between Banach spaces of functions.
By Trevor Harris, Yan Liu
arXiv:2501.18060v2 Announce Type: replace-cross
Abstract: Conformal inference provides a rigorous statistical framework for uncertainty quantification in machine learning, enabling well-calibrated pr...
By Teresa Bortolotti, Y. X. Rachel Wang, Xin Tong, Alessandra Menafoglio, Simone Vantini, Matteo Sesia
arXiv:2512.12749v3 Announce Type: replace-cross
Abstract: Learning surrogate models for physical systems with latent uncertainty remains challenging in data-scarce regimes: deterministic neural opera...
By Sahil Bhola, Karthik Duraisamy