Researchers have proposed several approaches for neural network (NN) based uncertainty quantification (UQ). However, most of the approaches are developed considering strong assumptions. Uncertainty quantification algorithms often perform poorly in an input domain and the reason for poor performance remains unknown. Therefore, we present a neural network training method that considers similar samples with sensitivity awareness in this paper. In the proposed NN training method for UQ, first, we train a shallow NN for the point prediction. Then, we compute the absolute differences between prediction and targets and train another NN for predicting those absolute differences or absolute errors. Domains with high average absolute errors represent a high uncertainty. In the next step, we select each sample in the training set one by one and compute both prediction and error sensitivities. Then we select similar samples with sensitivity consideration and save indexes of similar samples. The ranges of an input parameter become narrower when the output is highly sensitive to that parameter. After that, we construct initial uncertainty bounds (UB) by considering the distribution of sensitivity aware similar samples. Prediction intervals (PIs) from initial uncertainty bounds are larger and cover more samples than required. Therefore, we train bound correction NN. As following all the steps for finding UB for each sample requires a lot of computation and memory access, we train a UB computation NN. The UB computation NN takes an input sample and provides an uncertainty bound. The UB computation NN is the final product of the proposed approach. Scripts of the proposed method are available in the following GitHub repository: github.com/dipuk0506/UQ

翻译：研究者已提出多种基于神经网络的不确定性量化方法。然而，大多数方法在强假设条件下开发，且常出现输入域内性能不佳且原因不明的问题。为此，本文提出一种考虑敏感性感知的相似样本神经网络训练方法。在该不确定性量化神经网络训练方法中，首先训练浅层神经网络进行点预测，随后计算预测值与目标值的绝对差异，并训练另一神经网络预测这些绝对差异（即绝对误差）。平均绝对误差较高的域代表高不确定性区域。接着，逐一选取训练集中每个样本，同时计算其预测敏感性与误差敏感性，并基于敏感性约束筛选相似样本，保存其索引。当输出对某输入参数高度敏感时，该参数的取值范围会收窄。此后，通过考虑敏感性感知相似样本的分布构建初始不确定性边界。初始不确定性边界生成的预测区间覆盖范围大于实际需求，因此需训练边界校正神经网络。由于为每个样本确定不确定性边界需大量计算与内存访问，进一步训练不确定性边界计算神经网络。该网络以输入样本为参数直接输出不确定性边界，是所提方法的最终产物。方法代码已开源至GitHub仓库：github.com/dipuk0506/UQ