Abstract: We present a new framework for uncertainty quantification via information bottleneck (IB-UQ) in scientific machine learning tasks, including deep neural regression and neural operator learning. IB-UQ can provide uncertainty estimates in the label prediction by explicitly modeling the representation variables. Moreover, IB-UQ can be trained with noisy data and provide accurate predictions with reliable uncertainty estimates on unseen data. We also present the physics-informed version of IB-UQ for PDE-related problems. The capability of the proposed IB-UQ framework is demonstrated with numerical examples.

报告人简介：周涛，中国科学院数学与系统科学研究院研究员。主要研究方向为不确定性量化、偏微分方程数值方法以及时间并行算法等。国家高层次人家计划入选者。2018年担任国防科工局《核挑战专题》不确定性量化方向首席科学家。2022年获第三届王选杰出青年学者奖。现担任SIAM J Numer Anal.、SIAM J Sci Comput.、J Sci Comput.等十余种国内外权威期刊编委，并担任东亚工业与应用数学学会副主席及学会期刊EAJAM主编。