报告题目：Shock trace prediction by reduced models for a viscous stochastic Burgers equation

报告人：卢飞

单位：Johns Hopkins University

时间：8月17日 9:00

地点：学院南研

摘要：Viscous shocks are a particular type of extreme events in nonlinear multi-scale systems, and their representation requires small scales that are computationally costly to resolve. Model reduction has achieved great success in reducing the computational cost for efficient predictions of dynamics. A natural question is, can we predict random shocks with a reduced model? Yet, reduced models typically aim to approximate large-scale dominating dynamics, which do not resolve the small scales by design. To resolve this representation barrier, we introduce a new qualitative characterization of the space-time locations of shocks, named as the“shock trace”, via a space-time indicator function based on an empirical resolution-adaptive threshold. Different from the exact shocks, the shock traces can be captured within the representation capacity of the large scales, which facilitates the forecast of the timing and locations of the shocks utilizing reduced models. Within the context of a viscous stochastic Burgers equation, we show that a data-driven reduced model, in the form of nonlinear autoregression (NAR) time series models, can accurately predict the random shock traces, with relatively low rates of false predictions. The NAR model significantly outperforms the corresponding Galerkin truncated model in the scenario of either noiseless or noisy observations. The results illustrate the importance of the data-driven closure terms in the NAR model, which account for the effects of the unresolved small scale dynamics on the resolved ones due to nonlinear interactions.

简介：卢飞，美国约翰·霍普金斯大学副教授。本科毕业于华中科技大学，硕士毕业于中国科学院武汉物理与数学研究所，博士毕业于美国堪萨斯大学。后于劳伦斯伯克利国家实验室、加州大学伯克利分校从事研究工作。主要研究兴趣包括统计机器学习理论，反问题及正则化，复杂系统模型约化，数据同化及蒙特卡洛抽样，Malliavin分析、随机偏微分方程等。主持美国自然科学基金等。已在PNAS、PTRF、JMLR、SIAM、JFA、JCP等期刊发表20余篇论文.