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

A research team has applied split conformal prediction to neural operator-based physics simulation for the first time, delivering distribution-free prediction intervals with finite-sample coverage guarantees, according to a paper posted to arXiv [1]. Neural operators, including the Fourier Neural Operator, have become powerful surrogates for solving partial differential equations, offering speedups of several orders of magnitude over traditional numerical solvers [1]. Their deployment in safety-critical engineering — such as thermal management of electronic components and battery systems — demands not only accurate point predictions but also rigorous uncertainty guarantees [1]. Existing uncertainty quantification methods like Monte Carlo Dropout and Deep Ensembles provide only relative uncertainty estimates without formal coverage guarantees [1]. The new work addresses that gap by introducing 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 [1]. In full-scale experiments on steady-state heat conduction benchmarks, the method used a model with 33.7 million parameters, trained on 800 samples with five ensemble members on an NVIDIA V100 GPU [1]. It achieved 89.1 percent empirical coverage at a target alpha level of 0.1, while generating spatially adaptive prediction intervals that reflect the underlying physical uncertainty structure [1]. The researchers also developed an uncertainty decomposition framework that separates epistemic uncertainty, which accounted for 68 percent of the total, from aleatoric uncertainty at 32 percent, offering guidance for data collection and model improvement [1]. Physics-informed neural networks, which embed knowledge of physical laws described by PDEs into the learning process, have been used to enhance generalization when training data are scarce [3]. The prior knowledge acts as a regularization agent, limiting the space of admissible solutions and increasing the information content of available data [3]. The new conformal prediction approach builds on this lineage by adding formal coverage guarantees that earlier neural operator methods lacked [1]. The implementation is released as an open-source platform with REST API endpoints and interactive 3D visualization [1]. The paper was submitted on 7 June 2026 to the arXiv preprint server [1].