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Conference Paper: A Class of Data-driven Methods for Stochastic Partial Differential Equations
Title | A Class of Data-driven Methods for Stochastic Partial Differential Equations |
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Authors | |
Issue Date | 2016 |
Publisher | School of Mathematical Sciences, Fudan University. |
Citation | Joint Fudan-HKBU Workshop on Data Science, Fudan University, Shanghai, China, 4-7 May 2016 How to Cite? |
Abstract | We propose a data-driven stochastic method (DSM) to study stochastic partial differential equations (SPDEs) in the multiquery setting. An essential ingredient of the proposed method is to construct a data-driven stochastic basis under which the stochastic solutions to the SPDEs enjoy a compact representation for a broad range of forcing functions and/or boundary conditions. Our method consists of offline and online stages. A data-driven stochastic basis is computed in the offline stage using the Karhunen-Loeve (KL) expansion. In the online stage, we solve a relatively small number of coupled deterministic PDEs by projecting the stochastic solution into the data-driven stochastic basis constructed offline. Applications of DSM to stochastic elliptic problems show considerable computational savings over traditional methods even with a small number of queries. |
Persistent Identifier | http://hdl.handle.net/10722/239004 |
DC Field | Value | Language |
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dc.contributor.author | Zhang, Z | - |
dc.date.accessioned | 2017-02-27T09:46:33Z | - |
dc.date.available | 2017-02-27T09:46:33Z | - |
dc.date.issued | 2016 | - |
dc.identifier.citation | Joint Fudan-HKBU Workshop on Data Science, Fudan University, Shanghai, China, 4-7 May 2016 | - |
dc.identifier.uri | http://hdl.handle.net/10722/239004 | - |
dc.description.abstract | We propose a data-driven stochastic method (DSM) to study stochastic partial differential equations (SPDEs) in the multiquery setting. An essential ingredient of the proposed method is to construct a data-driven stochastic basis under which the stochastic solutions to the SPDEs enjoy a compact representation for a broad range of forcing functions and/or boundary conditions. Our method consists of offline and online stages. A data-driven stochastic basis is computed in the offline stage using the Karhunen-Loeve (KL) expansion. In the online stage, we solve a relatively small number of coupled deterministic PDEs by projecting the stochastic solution into the data-driven stochastic basis constructed offline. Applications of DSM to stochastic elliptic problems show considerable computational savings over traditional methods even with a small number of queries. | - |
dc.language | eng | - |
dc.publisher | School of Mathematical Sciences, Fudan University. | - |
dc.relation.ispartof | Fudan-HKBU Joint Workshop on Data Science, 2016 | - |
dc.title | A Class of Data-driven Methods for Stochastic Partial Differential Equations | - |
dc.type | Conference_Paper | - |
dc.identifier.email | Zhang, Z: zhangzw@hku.hk | - |
dc.identifier.authority | Zhang, Z=rp02087 | - |
dc.publisher.place | China | - |