报告题目： Variational Inverting Network for Statistical Inverse Problems of Partial Differential Equations

报 告 人：贾骏雄 教授 西安交通大学

报告时间：2023年 4 月 13 日 10:00-11:00

报告地点：腾讯会议 ID：650-107-514

会议链接：https://meeting.tencent.com/dm/DTyuBewqq14l

校内联系人：刁怀安 diao@jlu.edu.cn

报告摘要： For quantifying the uncertainties of the inverse problems governed by some partial differential equations (PDEs), the inverse problems are transformed into statistical inference problems based on Bayes' formula. Recently, infinite-dimensional Bayesian analysis methods have been introduced to give a rigorous characterization and construct dimension-independent algorithms. However, there are three major problems for current infinite-dimensional Bayesian methods: prior measures usually only behave like regularizers; complex noises are rarely considered; many computationally expensive forward PDEs need to be calculated for estimating posterior statistical quantities. To address these issues, we propose a general infinite-dimensional inference framework based on a detailed analysis of the infinite-dimensional variational inference method and the ideas of deep generative models that are popular in the machine learning community. Specifically, by introducing some measure equivalence assumptions, we derive the evidence lower bound in the infinite-dimensional setting and provide possible parametric strategies that yield a general inference framework named variational inverting network (VINet). This inference framework has the ability to encode prior and noise information from learning examples. In addition, relying on the power of deep neural networks, the posterior mean and variance can be efficiently generated in the inference stage in an explicit manner.

报告人简介：贾骏雄，西安交通大学教授、博士生导师。主要从事贝叶斯反问题理论与算法的研究。2017年获得陕西省优秀博士学位论文，2018入选西安交通大学第四届“十大学术新人”，2020年入选陕西高校“青年杰出人才支持计划”。已经在《SIAM J. Numer. Anal.》《SIAM J. Sci. Comput.》、《Inverse Problems》、《J. Funct. Anal.》等国内外刊物上发表30篇学术论文。主持国家自然科学基金3项，作为骨干成员参与科技部重点研发专项2项。