A new network approach to Bayesian inference in partial differential equations
Summary We introduce a novel numerical approach to parameter estimation in partial differential equations in a Bayesian inference context. The main idea is to translate the equation into a state‐discrete dynamic Bayesian network with the discretization of cellular probabilistic automata. There exist...
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| Veröffentlicht in: | International journal for numerical methods in engineering 2015-11, Vol.104 (5), p.313-329 |
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| container_end_page | 329 |
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| container_issue | 5 |
| container_start_page | 313 |
| container_title | International journal for numerical methods in engineering |
| container_volume | 104 |
| creator | Kohler, Dominic Marzouk, Youssef M. Müller, Johannes Wever, Utz |
| description | Summary
We introduce a novel numerical approach to parameter estimation in partial differential equations in a Bayesian inference context. The main idea is to translate the equation into a state‐discrete dynamic Bayesian network with the discretization of cellular probabilistic automata. There exists a vast pool of inference algorithms in the probabilistic graphical models field, which can be applied to the network.
In particular, we reformulate the parameter estimation as a filtering problem, discuss requirements for according tools in our specific setup, and choose the Boyen–Koller algorithm. To demonstrate our ideas, the scheme is applied to the problem of arsenate advection and adsorption in a water pipe: from measurements of the concentration of dissolved arsenate at the outflow boundary condition, we infer the strength of an arsenate source at the inflow boundary condition. Copyright © 2015 John Wiley & Sons, Ltd. |
| doi_str_mv | 10.1002/nme.4928 |
| format | Article |
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We introduce a novel numerical approach to parameter estimation in partial differential equations in a Bayesian inference context. The main idea is to translate the equation into a state‐discrete dynamic Bayesian network with the discretization of cellular probabilistic automata. There exists a vast pool of inference algorithms in the probabilistic graphical models field, which can be applied to the network.
In particular, we reformulate the parameter estimation as a filtering problem, discuss requirements for according tools in our specific setup, and choose the Boyen–Koller algorithm. To demonstrate our ideas, the scheme is applied to the problem of arsenate advection and adsorption in a water pipe: from measurements of the concentration of dissolved arsenate at the outflow boundary condition, we infer the strength of an arsenate source at the inflow boundary condition. Copyright © 2015 John Wiley & Sons, Ltd.</description><identifier>ISSN: 0029-5981</identifier><identifier>EISSN: 1097-0207</identifier><identifier>DOI: 10.1002/nme.4928</identifier><identifier>CODEN: IJNMBH</identifier><language>eng</language><publisher>Bognor Regis: Blackwell Publishing Ltd</publisher><subject>Algorithms ; Arsenates ; Bayesian analysis ; Boyen-Koller algorithm ; cellular probabilistic automata ; dynamic Bayesian networks ; hyperbolic ; Inference ; inverse ; Mathematical models ; Networks ; Partial differential equations ; probabilistic methods ; Probability theory</subject><ispartof>International journal for numerical methods in engineering, 2015-11, Vol.104 (5), p.313-329</ispartof><rights>Copyright © 2015 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c4348-81b85e850e4d3c3ed94417f4af52291ae8935d4a0ca2c3d19ae20aa21dd495573</citedby><cites>FETCH-LOGICAL-c4348-81b85e850e4d3c3ed94417f4af52291ae8935d4a0ca2c3d19ae20aa21dd495573</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fnme.4928$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fnme.4928$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>Kohler, Dominic</creatorcontrib><creatorcontrib>Marzouk, Youssef M.</creatorcontrib><creatorcontrib>Müller, Johannes</creatorcontrib><creatorcontrib>Wever, Utz</creatorcontrib><title>A new network approach to Bayesian inference in partial differential equations</title><title>International journal for numerical methods in engineering</title><addtitle>Int. J. Numer. Meth. Engng</addtitle><description>Summary
We introduce a novel numerical approach to parameter estimation in partial differential equations in a Bayesian inference context. The main idea is to translate the equation into a state‐discrete dynamic Bayesian network with the discretization of cellular probabilistic automata. There exists a vast pool of inference algorithms in the probabilistic graphical models field, which can be applied to the network.
In particular, we reformulate the parameter estimation as a filtering problem, discuss requirements for according tools in our specific setup, and choose the Boyen–Koller algorithm. To demonstrate our ideas, the scheme is applied to the problem of arsenate advection and adsorption in a water pipe: from measurements of the concentration of dissolved arsenate at the outflow boundary condition, we infer the strength of an arsenate source at the inflow boundary condition. Copyright © 2015 John Wiley & Sons, Ltd.</description><subject>Algorithms</subject><subject>Arsenates</subject><subject>Bayesian analysis</subject><subject>Boyen-Koller algorithm</subject><subject>cellular probabilistic automata</subject><subject>dynamic Bayesian networks</subject><subject>hyperbolic</subject><subject>Inference</subject><subject>inverse</subject><subject>Mathematical models</subject><subject>Networks</subject><subject>Partial differential equations</subject><subject>probabilistic methods</subject><subject>Probability theory</subject><issn>0029-5981</issn><issn>1097-0207</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp1kEtLxDAQx4MouD7Aj1Dw4qWayWObHFV0FXT14OsWxnaK0W67Jl3W_fZmVRQFD8O8fvyZ-TO2A3wfOBcH7YT2lRVmhQ2A2yLngherbJBWNtfWwDrbiPGZcwDN5YCND7OW5in6eRdeMpxOQ4flU9Z32REuKHpsM9_WFKgtKVXZFEPvsckqX39MPxp6nWHvuzZusbUam0jbX3mT3Z6e3Byf5RdXo_Pjw4u8VFKZ3MCj0WQ0J1XJUlJllYKiVlhrISwgGSt1pZCXKEpZgUUSHFFAVSmrdSE32d6nbjr3dUaxdxMfS2oabKmbRQfFMP0tjFyiu3_Q524W2nRdosCAlQDyR7AMXYyBajcNfoJh4YC7pbEuGeuWxiY0_0TnvqHFv5wbX5785n3s6e2bx_DihoUstLsfj5y4Ht09XA-P3IN8B0kwh-c</recordid><startdate>20151102</startdate><enddate>20151102</enddate><creator>Kohler, Dominic</creator><creator>Marzouk, Youssef M.</creator><creator>Müller, Johannes</creator><creator>Wever, Utz</creator><general>Blackwell Publishing Ltd</general><general>Wiley Subscription Services, Inc</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20151102</creationdate><title>A new network approach to Bayesian inference in partial differential equations</title><author>Kohler, Dominic ; Marzouk, Youssef M. ; Müller, Johannes ; Wever, Utz</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c4348-81b85e850e4d3c3ed94417f4af52291ae8935d4a0ca2c3d19ae20aa21dd495573</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Algorithms</topic><topic>Arsenates</topic><topic>Bayesian analysis</topic><topic>Boyen-Koller algorithm</topic><topic>cellular probabilistic automata</topic><topic>dynamic Bayesian networks</topic><topic>hyperbolic</topic><topic>Inference</topic><topic>inverse</topic><topic>Mathematical models</topic><topic>Networks</topic><topic>Partial differential equations</topic><topic>probabilistic methods</topic><topic>Probability theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kohler, Dominic</creatorcontrib><creatorcontrib>Marzouk, Youssef M.</creatorcontrib><creatorcontrib>Müller, Johannes</creatorcontrib><creatorcontrib>Wever, Utz</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>International journal for numerical methods in engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kohler, Dominic</au><au>Marzouk, Youssef M.</au><au>Müller, Johannes</au><au>Wever, Utz</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A new network approach to Bayesian inference in partial differential equations</atitle><jtitle>International journal for numerical methods in engineering</jtitle><addtitle>Int. J. Numer. Meth. Engng</addtitle><date>2015-11-02</date><risdate>2015</risdate><volume>104</volume><issue>5</issue><spage>313</spage><epage>329</epage><pages>313-329</pages><issn>0029-5981</issn><eissn>1097-0207</eissn><coden>IJNMBH</coden><abstract>Summary
We introduce a novel numerical approach to parameter estimation in partial differential equations in a Bayesian inference context. The main idea is to translate the equation into a state‐discrete dynamic Bayesian network with the discretization of cellular probabilistic automata. There exists a vast pool of inference algorithms in the probabilistic graphical models field, which can be applied to the network.
In particular, we reformulate the parameter estimation as a filtering problem, discuss requirements for according tools in our specific setup, and choose the Boyen–Koller algorithm. To demonstrate our ideas, the scheme is applied to the problem of arsenate advection and adsorption in a water pipe: from measurements of the concentration of dissolved arsenate at the outflow boundary condition, we infer the strength of an arsenate source at the inflow boundary condition. Copyright © 2015 John Wiley & Sons, Ltd.</abstract><cop>Bognor Regis</cop><pub>Blackwell Publishing Ltd</pub><doi>10.1002/nme.4928</doi><tpages>17</tpages></addata></record> |
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| language | eng |
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| source | Wiley Journals |
| subjects | Algorithms Arsenates Bayesian analysis Boyen-Koller algorithm cellular probabilistic automata dynamic Bayesian networks hyperbolic Inference inverse Mathematical models Networks Partial differential equations probabilistic methods Probability theory |
| title | A new network approach to Bayesian inference in partial differential equations |
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