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.
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: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.
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.
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.
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.
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.
arXiv:2507. 20975v5 Announce Type: replace-cross Abstract: Operator models are regression algorithms between Banach spaces of functions.
arXiv:2606. 17513v1 Announce Type: cross Abstract: Neural operators provide fast surrogates for PDEs but their deterministic predictions limit their use in tasks requiring uncertainty quantification (UQ), especially under geometric variability.
arXiv:2512. 13069v2 Announce Type: replace Abstract: Accurate aerodynamic prediction often relies on high-fidelity simulations; however, their prohibitive computational costs severely limit their applicability in data-driven modeling.
arXiv:2606. 24999v1 Announce Type: new Abstract: High-dimensional partial differential equations (PDEs) with unknown coefficients arise widely in scientific machine learning, including continuous-time reinforcement learning, yet solving them efficiently in a data-driven way remains challenging.
arXiv:2605. 00600v2 Announce Type: replace-cross Abstract: Deep neural networks achieve impressive results across diverse applications, yet their overconfidence on unseen inputs necessitates reliable epistemic uncertainty modeling.
arXiv:2606. 03600v1 Announce Type: cross Abstract: Standard conformal prediction (CP) procedures are typically formulated in terms of p-values, but reliance on p-values alone limits flexibility, for example, when combining dependent evidence across models or data splits.