This work introduces a method to equip data-driven polynomial chaos expansion surrogate models with intervals that quantify the predictive uncertainty of the surrogate. To that end, we integrate jackknife-based conformal prediction into regression-based polynomial chaos expansions. The jackknife algorithm uses leave-one-out residuals to generate predictive intervals around the predictions of the polynomial chaos surrogate. The jackknife+ extension additionally requires leave-one-out model predictions. The key to efficient implementation is to leverage the linearity of the polynomial chaos regression model, so that leave-one-out residuals and, if necessary, leave-one-out model predictions can be computed with analytical, closed-form expressions, thus eliminating the need for repeated model re-training. In addition to the efficient computation of the predictive intervals, a significant advantage of this approach is its data efficiency, as it requires no hold-out dataset for prediction interval calibration, thus allowing the entire dataset to be used for model training. The conformalized polynomial chaos expansion method is validated on several benchmark models, where the impact of training data volume on the predictive intervals is additionally investigated.

翻译：本研究提出一种方法，为数据驱动的多项式混沌展开代理模型配备能够量化代理预测不确定性的区间。为此，我们将基于刀切法的保形预测集成到基于回归的多项式混沌展开中。刀切法算法利用留一残差生成多项式混沌代理预测周围的预测区间。刀切法+扩展额外要求留一模型预测。高效实现的关键在于利用多项式混沌回归模型的线性特性，使得留一残差以及必要时留一模型预测可通过解析闭式表达式计算，从而无需重复模型重训练。除预测区间的高效计算外，该方法的一个显著优势在于其数据效率——它不需要用于预测区间校准的保留数据集，从而允许使用整个数据集进行模型训练。保形化多项式混沌展开方法在多个基准模型上得到验证，并额外研究了训练数据量对预测区间的影响。