AI 中文总结
该研究提出定向共形不确定性量化框架，通过数据驱动的非对称得分量化控制中物理预测器的非精度误差，缩小区间并支持多变量扩展，保留有限样本有效性。
AI 中文摘要
我们提出了一种用于量化控制中基于物理的预测器误差的共形预测框架，这类预测器因合成、验证及实时使用需求而偏好简单模型。由于这些模型是为适配预期应用而非追求最大预测精度而选择，其误差包含过程噪声与依赖状态的偏差。数据驱动的偏差估计定义了非对称非一致性得分：与学习到的偏差一致的误差，其惩罚小于相反方向同等大小的误差。这些集合保留在名义模型的误差坐标中且符合物理一致性，即包含原点处的一个球。该构造对偏差模型（核函数、神经网络或其他）无依赖，在可交换性下保留有限样本边际有效性，且在可表征的状态-输入区域内可证明地缩小区间。我们进一步表明，对于RKHS模型，功效函数为自适应得分设计提供局部置信度度量，并通过Minkowski-规范得分将该构造扩展到多变量情形，生成联合校准的干扰集合。
英文摘要
We propose a conformal prediction framework for quantifying the error of physics-based predictors used in control, where simple models are preferred for synthesis, certification, and real-time use. Because these models are selected for compatibility with the intended application rather than for maximal predictive accuracy, their error combines process noise with a state-dependent discrepancy. A data-driven discrepancy estimate defines an asymmetric nonconformity score: errors consistent with the learned discrepancy are penalized less than equally large in the opposite direction. The sets remain in the nominal model's error coordinates and are physics-consistent, i.e., they contain a ball at the origin. The construction is agnostic to the discrepancy model (kernel, neural-network, or other), preserves finite-sample marginal validity under exchangeability, and provably narrows the interval over a characterizable state-input region. We further show that, for RKHS models, the power function provides a local confidence measure for adaptive score design and we extend the construction to the multivariate case via a Minkowski-gauge score yielding a jointly calibrated disturbance set.
CommentsThis work has been submitted to the IEEE for possible publication
