为函数型代理模型构建可保证覆盖的预测集，提升科学机器学习可靠性。
Guaranteed prediction sets for functional surrogate models
- 基于SVD降维误差空间，用超椭体构造嵌套预测集
- 实现函数型模型预测集的严格统计覆盖保证
- 适用于神经算子等复杂模型，适合科研与工程验证
我们提出一种方法，为函数型机器学习代理模型（即在函数空间间映射的模型）生成具有统计保证的预测集，旨在构建可靠的偏微分方程模拟器。该方法在代理模型误差的低维表示（通过SVD获得）上构建嵌套预测集，并利用集合传播技术将其映射回预测空间，从而得到具备符合预测覆盖率保证的函数型预测集。采用超椭体作为集合基础，支持精确线性传播且对笛卡尔积封闭，适用于高维问题。该方法模型无关，可应用于复杂科学机器学习模型（如神经算子），也可用于简单场景。此外，我们引入了一种捕捉SVD截断误差的技术，确保方法的覆盖率保证不被破坏。
原文摘要 · Abstract (English)
We propose a method for obtaining statistically guaranteed prediction sets for functional machine learning methods: surrogate models which map between function spaces, motivated by the need to build reliable PDE emulators. The method constructs nested prediction sets on a low-dimensional representation (an SVD) of the surrogate model's error, and then maps these sets to the prediction space using set-propagation techniques. This results in prediction sets for functional surrogate models with conformal prediction coverage guarantees. We use zonotopes as basis of the set construction, which allow an exact linear propagation and are closed under Cartesian products, making them well-suited to this high-dimensional problem. The method is model agnostic and can thus be applied to complex Sci-ML models, including Neural Operators, but also in simpler settings. We also introduce a technique to capture the truncation error of the SVD, preserving the guarantees of the method.
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