We propose a novel framework for uncertainty quantification via information bottleneck (IB-UQ) for scientific machine learning tasks, including deep neural network (DNN) regression and neural operator learning (DeepONet). Specifically, we incorporate the bottleneck by a confidence-aware encoder, which encodes inputs into latent representations according to the confidence of the input data belonging to the region where training data is located, and utilize a Gaussian decoder to predict means and variances of outputs conditional on representation variables. Furthermore, we propose a data augmentation based information bottleneck objective which can enhance the quantification quality of the extrapolation uncertainty, and the encoder and decoder can be both trained by minimizing a tractable variational bound of the objective. In comparison to uncertainty quantification (UQ) methods for scientific learning tasks that rely on Bayesian neural networks with Hamiltonian Monte Carlo posterior estimators, the model we propose is computationally efficient, particularly when dealing with large-scale data sets. The effectiveness of the IB-UQ model has been demonstrated through several representative examples, such as regression for discontinuous functions, real-world data set regression, learning nonlinear operators for partial differential equations, and a large-scale climate model. The experimental results indicate that the IB-UQ model can handle noisy data, generate robust predictions, and provide confident uncertainty evaluation for out-of-distribution data.

翻译：摘要：我们提出了一种基于信息瓶颈的不确定性量化新框架（IB-UQ），用于科学机器学习任务，包括深度神经网络（DNN）回归和神经算子学习（DeepONet）。具体而言，我们通过一个置信度感知编码器引入瓶颈，该编码器根据输入数据属于训练数据所在区域的置信度将输入编码为潜在表示，并利用高斯解码器在表示变量条件下预测输出的均值和方差。此外，我们提出了一种基于数据增强的信息瓶颈目标函数，能够提升外推不确定性的量化质量，且编码器和解码器均可通过最小化该目标的可处理变分界进行联合训练。与依赖贝叶斯神经网络及哈密顿蒙特卡罗后验估计器的科学学习任务不确定性量化（UQ）方法相比，我们提出的模型在计算上更为高效，尤其适用于处理大规模数据集。通过多个代表性示例（如非连续函数回归、真实数据集回归、偏微分方程非线性算子学习以及大规模气候模型）验证了IB-UQ模型的有效性。实验结果表明，IB-UQ模型能够处理含噪数据、生成鲁棒预测，并为分布外数据提供可靠的不确定性评估。