学　术

　　人力资源部教师发展中心“学术沙龙”活动邀请中科院数学与系统科学研究院周涛副研究员到校交流，具体安排如下，欢迎广大师生参加！

　　一、主　题：Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems

　　二、主讲人：中科院数学与系统科学研究院　周涛 副研究员

　　三、时　间：2018年12月17日（周一）16：00

　　四、地　点：清水河校区主楼A1-513

　　五、主持人：数学科学学院　徐立伟 教授

　　六、交流内容：

　　The polynomial chaos (PC) expansion has been widely used as a surrogate model in the Bayesian inference to speed up the Markov chain Monte Carlo (MCMC) calculations. However, the use of a PC surrogate introduces the modeling error, that may severely distort the estimate of the posterior distribution. This error can be corrected by increasing the order of the PC expansion, but the cost for building the surrogate may increase dramatically.  In this talk, we seek to address this challenge by proposing an adaptive procedure to construct a multi-fidelity PC surrogate. This new strategy combines (a large number of) low-fidelity surrogate model evaluations and (a small number of) high-fidelity model evaluations, yielding an adaptive multi-fidelity approach. Here the low-fidelity surrogate is chosen as the prior-based PC surrogate, while the high-fidelity model refers to the true forward model. The key idea is to construct and refine the multi-fidelity approach over a sequence of samples adaptively determined form data, so that the approximation can eventually concentrate to the posterior distribution. We illustrate the performance of the proposed strategy through two nonlinear inverse problems. It is shown that the proposed adaptive multi-fidelity approach can improve significantly the accuracy, yet without a dramatic increase in the computational complexity. Applications to ensemble Kalman inversion will also be discussed.

　　七、主讲人简介：

　　周涛，中科院数学与系统科学研究院副研究员，曾在瑞士洛桑联邦工学院从事博士后研究，长期从事不确定性量化高精度算法研究。2016年曾获中国工业与应用数学学会优秀青年学者奖，2017年入选中科院数学与系统科学研究院“陈景润未来之星”称号，2018年获国家自然科学基金委优秀青年科学基金。现担任国际不确定性量化期刊Inter. J. for Uncertainty Quantification副主编（Associate Editor in Chief），东亚应用数学杂志East Asian Journal on Applied Mathematics执行主编（Managing Editor），同时担任期刊Communications in Computational Physics和Numer. Math.: Theory, Methods and Applications的编委。

 　八、主办单位：人力资源部教师发展中心

　　　　承办单位：数学科学学院

                         人力资源部教师发展中心

　　　　　　　　　　　　　　　　　　　　　2018年12月16日