mlsanityData to 14 Oct 2026

Split Conformal Prediction in the Function Space with Neural Operators

arXiv 2509.04623 ↗First posted 4 Sep 2025cs.LGcited by 4

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Abstract (arXiv)

Uncertainty quantification for neural operators remains an open problem in the infinite-dimensional setting due to the lack of finite-sample coverage guarantees over functional outputs. While conformal prediction offers finite-sample guarantees in finite-dimensional spaces, it does not directly extend to function-valued outputs. Existing approaches (Gaussian processes, Bayesian neural networks, and quantile-based operators) require strong distributional assumptions or yield conservative coverage. This work extends split conformal prediction to function spaces following a two step method. We first establish finite-sample coverage guarantees in a finite-dimensional space using a discretization map in the output function space. Then these guarantees are lifted to the function-space by considering the asymptotic convergence as the discretization is refined. To characterize the effect of resolution, we decompose the conformal radius into discretization, calibration, and misspecification components. This decomposition motivates a regression-based correction to transfer calibration across resolutions. Additionally, we propose two diagnostic metrics (conformal ensemble score and internal agreement) to quantify forecast degradation in autoregressive settings. Empirical results show that our method maintains calibrated coverage with less variation under resolution shifts and achieves better coverage in super-resolution tasks.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 20 of its 36 references that are in the map. First posted on arXiv 4 Sep 2025.

Builds on

20 of 36 references.

References · 20

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
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  8. 2021Is MC Dropout Bayesian?cited by 35
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  11. 2023Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operatorscited by 28
  12. 2024Calibrated Uncertainty Quantification for Operator Learning via Conformal Predictioncited by 26
8 more
  1. 2024Uncertainty quantification for data-driven weather modelscited by 26
  2. 2022Uncertainty Quantification for Traffic Forecasting: A Unified Approachcited by 22
  3. 2024Discretization Error of Fourier Neural Operatorscited by 22
  4. 2023IB-UQ: Information bottleneck based uncertainty quantification for neural function regression and neural operator learningcited by 18
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  6. 2024A Mathematical Analysis of Neural Operator Behaviorscited by 8
  7. 2022Distributional regression and its evaluation with the CRPS: Bounds and convergence of the minimax riskcited by 3
  8. 2025Multi-Scale Conformal Prediction: A Theoretical Framework with Coverage Guaranteescited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 4.

4 papers.

  1. 2026Geometry-Aware Uncertainty Quantification via Conformal Prediction on Manifoldscited by 2
  2. 2026Operator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regimecited by 1
  3. 2026Generative Neural Operators through Diffusion Last Layercited by 0
  4. 2026Conformal Uncertainty Quantification Guarantees for Neural Operatorscited by 0