Randomized neural operator for parametric PDEs with fast training and conformal uncertainty quantification
Provides an efficient, uncertainty-aware surrogate for many-query scientific workflows such as uncertainty quantification and design optimization.
PCA--RaNN reduces training time for parametric PDE surrogates by one to three orders of magnitude while maintaining competitive accuracy, and enables conformal uncertainty quantification via ensemble averaging.
Repeatedly solving parametric PDEs is essential for uncertainty quantification, design optimization and inverse problems, but conventional neural operators require expensive non-convex training. We introduce PCA--RaNN, a randomized latent neural operator that combines PCA-based dimensionality reduction with fixed random features and a closed-form least-squares readout. It recasts latent operator learning as fixed-feature linear regression, reducing training time by one to three orders of magnitude across benchmarks while maintaining competitive accuracy. We introduce an energy-matched scaling rule and a lightweight two-parameter BFGS refinement to correct suboptimal feature scales. Ensemble averaging reduces predictive variance. On Burgers, Darcy, Navier--Stokes and backward heat equation benchmarks, PCA--RaNN provides a favorable speed--accuracy trade-off against operator-learning baselines. The ensemble supports split-conformal prediction intervals, and the linear readout enables rapid online adaptation via recursive least squares without retraining hidden features. This provides an efficient, uncertainty-aware surrogate for many-query scientific workflows.