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.
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×.
arXiv:2505. 08784v2 Announce Type: replace-cross Abstract: As machine learning (ML) enters high-stakes domains, trustworthy uncertainty quantification (UQ) is essential for safety.
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.
The paper investigates how pre‑training strategy, dataset size, and domain affect uncertainty estimation in vision medical foundation models. It compares point‑prediction calibration with conformal (region) prediction across retinal, histopathological, and chest X‑ray models, finding that domain‑specific, self‑supervised pre‑training yields better calibration and more efficient conformal sets. The study shows that standard recalibration alone cannot fully reconcile uncertainty differences between models trained on different data sources.
arXiv:2609.37298v1 Announce Type: new Abstract: Conformal prediction provides set-valued predictions with distribution-free coverage guarantees, making it attractive for high-stakes image classificat...
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.
arXiv:2507. 20975v5 Announce Type: replace-cross Abstract: Operator models are regression algorithms between Banach spaces of functions.
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...
arXiv:2608.24518v1 Announce Type: new Abstract: Uncertainty Quantification (UQ) plays a vital role in enhancing the reliability of deep learning model predictions, especially in scenarios with high-d...
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.
Uncertainty Quantification (UQ) plays a vital role in enhancing the reliability of deep learning model predictions, especially in scenarios with high-dimensional output spaces. This paper addresses th...