mlsanityData to 14 Oct 2026

Locally Adaptive Conformal Inference for Operator Models

arXiv 2507.20975 ↗First posted 28 Jul 2025stat.ML cs.LGcited by 2

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Abstract (arXiv)

Operator models are regression algorithms between Banach spaces of functions. They have become an increasingly critical tool for spatiotemporal forecasting and physics emulation, especially in high-stakes scenarios where robust, calibrated uncertainty quantification is required. We introduce Local Sliced Conformal Inference (LSCI), a distribution-free framework for generating function-valued, locally adaptive prediction sets for operator models. We prove finite-sample validity and derive a data-dependent upper bound on the coverage gap under local exchangeability. On synthetic Gaussian-process tasks and real applications (air quality monitoring, energy demand forecasting, and weather prediction), LSCI yields tighter sets with stronger adaptivity compared to conformal baselines. We also empirically demonstrate robustness against biased predictions and certain out-of-distribution noise regimes.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 33 of its 70 references that are in the map. First posted on arXiv 28 Jul 2025.

Builds on

33 of 70 references.

References · 33

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  2. 2021Convex optimizationcited by 2,515
  3. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  4. 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 776
  5. 2016Distribution-Free Predictive Inference For Regressioncited by 668
  6. 2019Conformalized Quantile Regressioncited by 629
  7. 2022Conformal prediction beyond exchangeabilitycited by 355
  8. 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 303
  9. 2021Distribution-Free, Risk-Controlling Prediction Setscited by 288
  10. 2020Model Reduction and Neural Networks for Parametric PDEscited by 258
  11. 2023Spherical Fourier Neural Operators: Learning Stable Dynamics on the Spherecited by 233
  12. 2021Localized Conformal Prediction: A Generalized Inference Framework for Conformal Predictioncited by 114
21 more
  1. 2022Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imagingcited by 107
  2. 2020The Random Feature Model for Input-Output Maps between Banach Spacescited by 90
  3. 2013A Conformal Prediction Approach to Explore Functional Datacited by 86
  4. 2024Operator Learning: Algorithms and Analysiscited by 85
  5. 2023Super-Resolution Neural Operatorcited by 49
  6. 2023Conformal prediction with local weights: randomization enables local guaranteescited by 48
  7. 2022Real-time high-resolution CO2 geological storage prediction using nested Fourier neural operatorscited by 47
  8. 2023Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equationcited by 32
  9. 2021Conformal Prediction Bands for Multivariate Functional Datacited by 29
  10. 2024Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networkscited by 28
  11. 2024Calibrated Uncertainty Quantification for Operator Learning via Conformal Predictioncited by 26
  12. 2022Approximate Bayesian Neural Operators: Uncertainty Quantification for Parametric PDEscited by 25
  13. 2022Adaptive Bias Correction for Improved Subseasonal Forecastingcited by 19
  14. 2021Known Operator Learning and Hybrid Machine Learning in Medical Imaging -- A Review of the Past, the Present, and the Futurecited by 18
  15. 2025Probabilistic neural operators for functional uncertainty quantificationcited by 18
  16. 2023Do AI models produce better weather forecasts than physics-based models? A quantitative evaluation case study of Storm Ciar'ancited by 12
  17. 2024Linearization Turns Neural Operators into Function-Valued Gaussian Processescited by 12
  18. 2022Variational Bayes Deep Operator Network: A data-driven Bayesian solver for parametric differential equationscited by 11
  19. 2019Elastic depths for detecting shape anomalies in functional datacited by 5
  20. 2024Conformalized Prediction of Post-Fault Voltage Trajectories Using Pre-trained and Finetuned Attention-Driven Neural Operatorscited by 5
  21. 2024Quantifying uncertainty in climate projections with conformal ensemblescited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Flow-Based Conformal Predictive Distributionscited by 2
  2. 2026Sample-Efficient Generative Conformal Predictioncited by 0