Numerous studies have focused on learning and understanding the dynamics of physical systems from video data, such as spatial intelligence. Artificial intelligence requires quantitative assessments of the uncertainty of the model to ensure reliability. However, there is still a relative lack of systematic assessment of the uncertainties, particularly the uncertainties of the physical data. Our motivation is to introduce conformal prediction into the uncertainty assessment of dynamical systems, providing a method supported by theoretical guarantees. This paper uses the conformal prediction method to assess uncertainties with benchmark operator learning methods. We have also compared the Monte Carlo Dropout and Ensemble methods in the partial differential equations dataset, effectively evaluating uncertainty through straight roll-outs, making it ideal for time-series tasks.

翻译：众多研究聚焦于从视频数据中学习和理解物理系统的动态特性，例如空间智能。人工智能需要对模型的不确定性进行量化评估以确保可靠性。然而，目前仍相对缺乏对不确定性的系统性评估，特别是对物理数据不确定性的评估。我们的研究动机是将保形预测引入动态系统的不确定性评估中，提供一种具有理论保证支撑的方法。本文采用保形预测方法，结合基准算子学习方法进行不确定性评估。我们还在偏微分方程数据集中比较了蒙特卡洛Dropout与集成方法，通过直接推演有效评估了不确定性，使其特别适用于时间序列任务。