Conformal Prediction for Neural Operators: Distribution-Free Uncertainty Quantification in Physics Simulation

• URL: http://arxiv.org/abs/2606.09923v1
• Date: Sun, 07 Jun 2026 08:52:38 GMT
• Title: Conformal Prediction for Neural Operators: Distribution-Free Uncertainty Quantification in Physics Simulation
• Abstract summary: We propose the first application of split conformal prediction to neural operator-based physics simulation.<n>Our method achieves 89.1% empirical coverage at the target level of alpha=0.1.<n>Our method is implemented in an open-source platform with REST API endpoints and interactive 3D visualization.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Neural operators such as the Fourier Neural Operator (FNO) have emerged as powerful surrogates for solving partial differential equations (PDEs), achieving speedups of several orders of magnitude over traditional numerical solvers. However, deploying these models in safety-critical engineering applications -- such as thermal management of electronic components and battery systems -- requires not only accurate point predictions but also rigorous uncertainty guarantees. Existing uncertainty quantification (UQ) methods for neural operators, including Monte Carlo Dropout and Deep Ensembles, provide only relative uncertainty estimates without formal coverage guarantees. In this work, we propose the first application of split conformal prediction to neural operator-based physics simulation, providing distribution-free prediction intervals with finite-sample coverage guarantees. We further introduce a normalized conformal prediction scheme that leverages MC Dropout uncertainty to produce adaptive-width intervals, yielding tighter intervals in regions of low uncertainty and wider intervals where the model is less certain. Full-scale experiments (33.7M parameters, 800 training samples, 5 ensemble members, NVIDIA V100) on steady-state heat conduction benchmarks demonstrate that our method achieves 89.1% empirical coverage at the target level of alpha=0.1, while producing spatially adaptive prediction intervals that reflect the underlying physical uncertainty structure. We also provide an uncertainty decomposition framework that separates epistemic uncertainty (68% of total) from aleatoric uncertainty (32% of total), offering actionable guidance for data collection and model improvement. Our method is implemented in an open-source platform with REST API endpoints and interactive 3D visualization.

Related papers

• Structure-Aware Epistemic Uncertainty Quantification for Neural Operator PDE Surrogates [10.39662017167378]
  Uncertainty quantification (UQ) must be both computationally efficient and spatially faithful.<n>We propose a structure-aware UQ scheme that exploits the modular anatomy common to modern NOs.<n> Experiments on challenging PDE benchmarks demonstrate that the proposed structure-aware design yields more reliable coverage, tighter bands, and improved residual-uncertainty alignment.
  arXiv  Detail & Related papers  (2026-02-24T10:17:24Z)
• Bridging the Gap Between Bayesian Deep Learning and Ensemble Weather Forecasts [100.26854618129039]
  Weather forecasting is fundamentally challenged by the chaotic nature of the atmosphere.<n>Recent advances in Bayesian Deep Learning (BDL) offer a promising but often disconnected alternative.<n>We bridge these paradigms through a unified hybrid BDL framework for ensemble weather forecasting.
  arXiv  Detail & Related papers  (2025-11-18T07:49:52Z)
• Calibrated Decomposition of Aleatoric and Epistemic Uncertainty in Deep Features for Inference-Time Adaptation [3.018583625592182]
  Most estimators collapse all uncertainty modes into a single confidence score, preventing reliable reasoning about when to allocate more compute or adjust inference.<n>We introduce Uncertainty-Guided Inference-Time Selection, a lightweight inference time framework that disentangles aleatoric (data-driven) and model-driven uncertainty directly in deep feature space.
  arXiv  Detail & Related papers  (2025-11-15T23:47:30Z)
• A Conformal Prediction Framework for Uncertainty Quantification in Physics-Informed Neural Networks [0.9613011825024471]
  PINNs have emerged as a powerful framework for solving PDEs.<n>Existing uncertainty quantification approaches for PINNs generally lack rigorous statistical guarantees.<n>We introduce a distribution-free conformal prediction framework for UQ in PINNs.
  arXiv  Detail & Related papers  (2025-09-17T06:12:48Z)
• Bayesian optimized deep ensemble for uncertainty quantification of deep neural networks: a system safety case study on sodium fast reactor thermal stratification modeling [10.055838489452817]
  Deep ensembles (DEs) are efficient and scalable methods for uncertainty quantification (UQ) in Deep Neural Networks (DNNs)<n>We propose a novel method that combines Bayesian optimization (BO) with DE, referred to as BODE, to enhance both predictive accuracy and UQ.<n>We apply BODE to a case study involving a Densely connected Convolutional Neural Network (DCNN) trained on computational fluid dynamics (CFD) data to predict eddy viscosity in sodium fast reactor thermal stratification modeling.
  arXiv  Detail & Related papers  (2024-12-11T21:06:50Z)
• Generative Conformal Prediction with Vectorized Non-Conformity Scores [6.059745771017814]
  Conformal prediction provides model-agnostic uncertainty quantification with guaranteed coverage.<n>We propose a generative conformal prediction framework with vectorized non-conformity scores.<n>We construct adaptive uncertainty sets using density-ranked uncertainty balls.
  arXiv  Detail & Related papers  (2024-10-17T16:37:03Z)
• Calibrated Uncertainty Quantification for Operator Learning via Conformal Prediction [95.75771195913046]
  We propose a risk-controlling quantile neural operator, a distribution-free, finite-sample functional calibration conformal prediction method. We provide a theoretical calibration guarantee on the coverage rate, defined as the expected percentage of points on the function domain. Empirical results on a 2D Darcy flow and a 3D car surface pressure prediction task validate our theoretical results.
  arXiv  Detail & Related papers  (2024-02-02T23:43:28Z)
• Score Matching-based Pseudolikelihood Estimation of Neural Marked Spatio-Temporal Point Process with Uncertainty Quantification [59.81904428056924]
  We introduce SMASH: a Score MAtching estimator for learning markedPs with uncertainty quantification. Specifically, our framework adopts a normalization-free objective by estimating the pseudolikelihood of markedPs through score-matching. The superior performance of our proposed framework is demonstrated through extensive experiments in both event prediction and uncertainty quantification.
  arXiv  Detail & Related papers  (2023-10-25T02:37:51Z)
• NUQ: Nonparametric Uncertainty Quantification for Deterministic Neural Networks [151.03112356092575]
  We show the principled way to measure the uncertainty of predictions for a classifier based on Nadaraya-Watson's nonparametric estimate of the conditional label distribution. We demonstrate the strong performance of the method in uncertainty estimation tasks on a variety of real-world image datasets.
  arXiv  Detail & Related papers  (2022-02-07T12:30:45Z)
• Dense Uncertainty Estimation [62.23555922631451]
  In this paper, we investigate neural networks and uncertainty estimation techniques to achieve both accurate deterministic prediction and reliable uncertainty estimation. We work on two types of uncertainty estimations solutions, namely ensemble based methods and generative model based methods, and explain their pros and cons while using them in fully/semi/weakly-supervised framework.
  arXiv  Detail & Related papers  (2021-10-13T01:23:48Z)
• Unlabelled Data Improves Bayesian Uncertainty Calibration under Covariate Shift [100.52588638477862]
  We develop an approximate Bayesian inference scheme based on posterior regularisation. We demonstrate the utility of our method in the context of transferring prognostic models of prostate cancer across globally diverse populations.
  arXiv  Detail & Related papers  (2020-06-26T13:50:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.