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Certified Offline-Free Reduced Basis methods for stochastic differential equations driven by arbitrary types of noises
时间  Datetime
2019-07-13 10:00 — 11:00 
地点  Venue
639
报告人  Speaker
Yanlai Chen
单位  Affiliation
UMass Dartmouth
邀请人  Host
Zhenli Xu
报告摘要  Abstract

In scenarios where a large number of numerical solutions to a sequence of problems are desired in a fast/real-time fashion, Reduced basis method (RBM) can potentially improve efficiency by several orders of magnitudes. It leverages a machine learning philosophy, an offline-online procedure, and the recognition that the solution space of the concerned sequence of problems can be well approximated by a smaller space in a tailored fashion.

After a brief introduction of RBM, this talk presents a new method tailored for the linear ordinary and partial differential equations driven by arbitrary types of noise. Main novel ingredients are a new space-time-like treatment for ODEs and PDEs based on time-stepping, an accurate yet efficient compression technique for the spatial component of the spacetime snapshots of RBM, a non-conventional parameterization of a non-parametric problem, and finally a RBM that is free of any dedicated offline procedure and online efficient.