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Title: A Data-Driven Stochastic Multiscale Method
Originating Office: IAS
Speaker: Hou, Thomas
Issue Date: 17-Sep-2010
Event Date: 17-Sep-2010
Group/Series/Folder: Record Group 8.15 - Institute for Advanced Study
Series 3 - Audio-visual Materials
Location: 8.15:3 box 1.5
Notes: IAS Distinguished Lecture.
Abstract: Prof Hou introduces a data-driven stochastic multiscale method to solve stochastic PDEs with high dimensionality in probability space. This method consists of two steps: Offline and Online. In the Offline step, he constructs a multiscale stochastic basis by approximating the covariance of the solution of the SPDE using Monte Carlo methods. In the Online step, he represents the stochastic solution as a truncated expansion using the multiscale stochastic basis. By solving a set of coupled PDEs of deterministic coefficients, he obtains the numerical solutions to SPDEs. One important property of this method is that the stochastic basis obtained in the offline computation can be used repeatedly in online computation for a large class of stochastic problems with different deterministic forcing coefficients or boundary conditions. This method effectively reduces the dimension of the stochastic PDEs. As a consequence, much smaller number of basis is required in the online computation to achieve the same level of error tolerance compared to the (generalized) polynomial chaos method or Wiener-Chaos Expansion method. Some numerical results will be presented to demonstrate the effectiveness of the method.
Duration: 82 min.
Appears in Series:8.15:3 - Audio-visual Materials
Videos for Public -- Distinguished Lectures