報告題目： Variational Inverting Network for Statistical Inverse Problems of Partial Differential Equations
報 告 人：賈駿雄 教授 西安交通大學
報告時間：2023年 4 月 13 日 10:00-11:00
報告地點：騰訊會議 ID：650-107-514
會議鍊接：https://meeting.tencent.com/dm/DTyuBewqq14l
校内聯系人：刁懷安 diao@jlu.edu.cn
報告摘要： 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.
報告人簡介：賈駿雄，西安交通大學教授、博士生導師。主要從事貝葉斯反問題理論與算法的研究。2017年獲得陝西省優秀博士學位論文，2018入選西安交通大學第四屆“十大學術新人”，2020年入選陝西高校“青年傑出人才支持計劃”。已經在《SIAM J. Numer. Anal.》《SIAM J. Sci. Comput.》、《Inverse Problems》、《J. Funct. Anal.》等國内外刊物上發表30篇學術論文。主持國家自然科學基金3項，作為骨幹成員參與科技部重點研發專項2項。
