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