Operator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regime
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. While neural operators provide fast surrogates for expensive PDE solvers, they do not by themselves provide calibrated uncertainty for spatiotemporal field predictions. Our approach wraps a trained Fourier Neural Operator (FNO) with split conformal prediction and constructs the local uncertainty scale by comparing the predictions of two operators trained on nearly identical datasets: one on the original labels and one on labels perturbed by small Gaussian noise. We consider this procedure in the data-scarce regi...
| Authors | Weinan Wang, Bowen Gang, Hao Deng |
|---|---|
| Primary category | cs.LG |
| Published | 7 June 2026 |
| Last updated at source | 7 June 2026 |
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