arXiv Machine Learning By Zirui Deng, Jingbo Sun, Deyu Meng, Fei Wang

Randomized neural operator for parametric PDEs with fast training and conformal uncertainty quantification

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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.

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arXiv Machine Learning
Sep 14

Physics-Informed Conformal Prediction: Embedding PDE Consistency into Distribution-Free Uncertainty Quantification for Neural Operators

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