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Threshold-Aware Conformal Routing

arXiv 2610.02487 ↗First posted 1 Oct 2026cs.LG cs.CEcited by 0

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Abstract (arXiv)

High-fidelity simulations are essential to scientific and engineering design, but can be expensive to run repeatedly. Learned surrogates offer a faster alternative, yet their higher errors may alter downstream decisions. This accuracy-speed tradeoff creates a need to determine whether a surrogate can be used or the full simulator remains necessary. We study decisions determined by whether a scalar quantity of interest lies above or below a fixed threshold. For each input, we use the surrogate when its conformal interval lies entirely on one side of the threshold and route the input to simulation when the interval intersects it. Standard conformal prediction constructs intervals without reference to the downstream decision threshold: even a narrow interval near the threshold can cross it and trigger simulation, whereas a wider interval farther away can remain entirely on one side and require no simulation. We introduce Threshold-Aware Conformal Routing (TACR), which learns an input-dependent scale using a threshold-aware objective that concentrates interval tightness near the decision boundary. Exact split-conformal calibration on held-out data preserves distribution-free marginal coverage, which also upper-bounds the probability of an incorrect threshold decision that is not routed. Across various scientific and engineering datasets, TACR reduces simulator deferrals by 14-75% relative to standard conformal prediction at the same coverage target. Against a variant without threshold-local weighting but with similar predictor accuracy, TACR further reduces deferrals by 10-24% on four datasets. These results show that optimizing interval allocation for routing can reduce simulator calls without weakening the standard conformal guarantee.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 31 of its 40 references that are in the map. First posted on arXiv 1 Oct 2026.

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31 of 40 references.

References · 31

  1. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,448
  2. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,926
  3. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  4. 2020Learning Mesh-Based Simulation with Graph Networkscited by 868
  5. 2019Conformalized Quantile Regressioncited by 629
  6. 2022PDEBENCH: An Extensive Benchmark for Scientific Machine Learningcited by 413
  7. 2019Deep Evidential Regressioncited by 355
  8. 2024Transolver: A Fast Transformer Solver for PDEs on General Geometriescited by 326
  9. 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 303
  10. 2020Consistent Estimators for Learning to Defer to an Expertcited by 271
  11. 2017Predict Responsibly: Improving Fairness and Accuracy by Learning to Defercited by 233
  12. 2021Learning Optimal Conformal Classifierscited by 112
19 more
  1. 2025Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometriescited by 97
  2. 2022AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutionscited by 82
  3. 2025AB-UPT: Scaling Neural CFD Surrogates for High-Fidelity Automotive Aerodynamics Simulations via Anchored-Branched Universal Physics Transformerscited by 53
  4. 2023Conformal Decision Theory: Safe Autonomous Decisions from Imperfect Predictionscited by 50
  5. 2024Boosted Conformal Prediction Intervalscited by 27
  6. 2025DoMINO: A Decomposable Multi-scale Iterative Neural Operator for Modeling Large Scale Engineering Simulationscited by 27
  7. 2024Calibrated Uncertainty Quantification for Operator Learning via Conformal Predictioncited by 26
  8. 2022Approximate Bayesian Neural Operators: Uncertainty Quantification for Parametric PDEscited by 25
  9. 2025GeoTransolver: Learning Physics on Irregular Domains Using Multi-scale Geometry Aware Physics Attention Transformercited by 23
  10. 2024X-MeshGraphNet: Scalable Multi-Scale Graph Neural Networks for Physics Simulationcited by 22
  11. 2024Using Uncertainty Quantification to Characterize and Improve Out-of-Domain Learning for PDEscited by 15
  12. 2024AhmedML: High-Fidelity Computational Fluid Dynamics Dataset for Incompressible, Low-Speed Bluff Body Aerodynamicscited by 15
  13. 2024End-to-End Conformal Calibration for Optimization Under Uncertaintycited by 15
  14. 2024Utility-Directed Conformal Prediction: A Decision-Aware Framework for Actionable Uncertainty Quantificationcited by 13
  15. 2024Conformal Risk Minimization with Variance Reductioncited by 11
  16. 2023Reliable Prediction Intervals with Directly Optimized Inductive Conformal Regression for Deep Learningcited by 5
  17. 2024Conformalized Selective Regressioncited by 5
  18. 2026Co-optimization for Adaptive Conformal Predictioncited by 2
  19. 2026Proactive Routing to Interpretable Surrogates with Distribution-Free Safety Guaranteescited by 2

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