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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...