给神经算子加不确定度保证，无需假设分布就能可靠预测物理模拟结果。
Conformal Prediction for Neural Operators: Distribution-Free Uncertainty Quantification in Physics Simulation
- 用分割保形预测法为神经算子生成无分布假设的置信区间。
- 在热传导测试中达到89.1%的实际覆盖率达目标水平（α=0.1）。
- 能自适应调整区间宽度，区分模型不确定性和物理随机性，适合工程安全场景。
神经算子（如FNO）作为偏微分方程的高效替代求解器，可实现数个数量级的速度提升。但在电子器件热管理、电池系统等安全关键领域部署时，仅靠点预测不足，还需严格不确定性保障。现有不确定性量化方法（如蒙特卡洛丢弃、深度集成）仅提供相对不确定性，缺乏形式化覆盖率保证。本文首次将分割保形预测应用于神经算子物理模拟，提供无分布假设的预测区间及有限样本覆盖率。进一步提出归一化保形方案，利用蒙特卡洛丢弃不确定性生成自适应宽度区间，在低不确定性区域更紧致，高不确定性区域更宽泛。大规模实验（3370万参数，800个训练样本，5个集成成员，NVIDIA V100）显示，方法在α=0.1目标下实现89.1%的实测覆盖率，且区间空间分布反映物理不确定性结构。我们还提出不确定性分解框架，分离出认知不确定性（占总不确定性的68%）与随机不确定性（32%），为数据收集和模型优化提供可操作指导。代码开源，支持REST API与交互式3D可视化。
原文摘要 · Abstract (English)
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.
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