Randomized neural operator for parametric PDEs with fast training and conformal uncertainty quantification
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. Ensemb...
| Authors | Zirui Deng, Jingbo Sun, Deyu Meng et al. |
|---|---|
| Primary category | cs.LG |
| Published | 28 June 2026 |
| Last updated at source | 28 June 2026 |
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