Polynomial Neural Networks and Taylor maps for Dynamical Systems Simulation and Learning
24th European Conference on Artificial Intelligence - ECAI 2020 The connection of Taylor maps and polynomial neural networks (PNN) to solve ordinary differential equations (ODEs) numerically is considered. Having the system of ODEs, it is possible to calculate weights of PNN that simulates the dynam...
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| creator | Ivanov, Andrei Golovkina, Anna Iben, Uwe |
| description | 24th European Conference on Artificial Intelligence - ECAI 2020 The connection of Taylor maps and polynomial neural networks (PNN) to solve
ordinary differential equations (ODEs) numerically is considered. Having the
system of ODEs, it is possible to calculate weights of PNN that simulates the
dynamics of these equations. It is shown that proposed PNN architecture can
provide better accuracy with less computational time in comparison with
traditional numerical solvers. Moreover, neural network derived from the ODEs
can be used for simulation of system dynamics with different initial
conditions, but without training procedure. On the other hand, if the equations
are unknown, the weights of the PNN can be fitted in a data-driven way. In the
paper we describe the connection of PNN with differential equations in a
theoretical way along with the examples for both dynamics simulation and
learning with data. |
| doi_str_mv | 10.48550/arxiv.1912.09986 |
| format | Article |
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ordinary differential equations (ODEs) numerically is considered. Having the
system of ODEs, it is possible to calculate weights of PNN that simulates the
dynamics of these equations. It is shown that proposed PNN architecture can
provide better accuracy with less computational time in comparison with
traditional numerical solvers. Moreover, neural network derived from the ODEs
can be used for simulation of system dynamics with different initial
conditions, but without training procedure. On the other hand, if the equations
are unknown, the weights of the PNN can be fitted in a data-driven way. In the
paper we describe the connection of PNN with differential equations in a
theoretical way along with the examples for both dynamics simulation and
learning with data.</description><identifier>DOI: 10.48550/arxiv.1912.09986</identifier><language>eng</language><subject>Computer Science - Neural and Evolutionary Computing ; Computer Science - Numerical Analysis ; Mathematics - Numerical Analysis</subject><creationdate>2019-12</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1912.09986$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1912.09986$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Ivanov, Andrei</creatorcontrib><creatorcontrib>Golovkina, Anna</creatorcontrib><creatorcontrib>Iben, Uwe</creatorcontrib><title>Polynomial Neural Networks and Taylor maps for Dynamical Systems Simulation and Learning</title><description>24th European Conference on Artificial Intelligence - ECAI 2020 The connection of Taylor maps and polynomial neural networks (PNN) to solve
ordinary differential equations (ODEs) numerically is considered. Having the
system of ODEs, it is possible to calculate weights of PNN that simulates the
dynamics of these equations. It is shown that proposed PNN architecture can
provide better accuracy with less computational time in comparison with
traditional numerical solvers. Moreover, neural network derived from the ODEs
can be used for simulation of system dynamics with different initial
conditions, but without training procedure. On the other hand, if the equations
are unknown, the weights of the PNN can be fitted in a data-driven way. In the
paper we describe the connection of PNN with differential equations in a
theoretical way along with the examples for both dynamics simulation and
learning with data.</description><subject>Computer Science - Neural and Evolutionary Computing</subject><subject>Computer Science - Numerical Analysis</subject><subject>Mathematics - Numerical Analysis</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj81OxCAYRdm4MKMP4EpeoBUoICzN-Js0ajJduGu-AmOIBSbQUfv21urq3MW9NzkIXVBScyUEuYL87T9rqimridZKnqK31zTOMQUPI352x7xi-kr5o2CIFncwjynjAIeC90u4nSMEb5babi6TCwXvfDiOMPkU10HrIEcf38_QyR7G4s7_uUHd_V23fazal4en7U1bgbyWlWSq0WLgkitFHeVgBZHMGqXtAA4YIbyhkjEihTSNo0YwIgZjFSix9HWzQZd_t6taf8g-QJ77X8V-VWx-ABFyS_s</recordid><startdate>20191219</startdate><enddate>20191219</enddate><creator>Ivanov, Andrei</creator><creator>Golovkina, Anna</creator><creator>Iben, Uwe</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20191219</creationdate><title>Polynomial Neural Networks and Taylor maps for Dynamical Systems Simulation and Learning</title><author>Ivanov, Andrei ; Golovkina, Anna ; Iben, Uwe</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a676-628395b464881e14ad5062dc89dbaea2004316220656c3e1c5205bcd8a851e193</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Computer Science - Neural and Evolutionary Computing</topic><topic>Computer Science - Numerical Analysis</topic><topic>Mathematics - Numerical Analysis</topic><toplevel>online_resources</toplevel><creatorcontrib>Ivanov, Andrei</creatorcontrib><creatorcontrib>Golovkina, Anna</creatorcontrib><creatorcontrib>Iben, Uwe</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Ivanov, Andrei</au><au>Golovkina, Anna</au><au>Iben, Uwe</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Polynomial Neural Networks and Taylor maps for Dynamical Systems Simulation and Learning</atitle><date>2019-12-19</date><risdate>2019</risdate><abstract>24th European Conference on Artificial Intelligence - ECAI 2020 The connection of Taylor maps and polynomial neural networks (PNN) to solve
ordinary differential equations (ODEs) numerically is considered. Having the
system of ODEs, it is possible to calculate weights of PNN that simulates the
dynamics of these equations. It is shown that proposed PNN architecture can
provide better accuracy with less computational time in comparison with
traditional numerical solvers. Moreover, neural network derived from the ODEs
can be used for simulation of system dynamics with different initial
conditions, but without training procedure. On the other hand, if the equations
are unknown, the weights of the PNN can be fitted in a data-driven way. In the
paper we describe the connection of PNN with differential equations in a
theoretical way along with the examples for both dynamics simulation and
learning with data.</abstract><doi>10.48550/arxiv.1912.09986</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Neural and Evolutionary Computing Computer Science - Numerical Analysis Mathematics - Numerical Analysis |
| title | Polynomial Neural Networks and Taylor maps for Dynamical Systems Simulation and Learning |
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