The Euler-Type Universal Numerical Integrator (E-TUNI) with Backward Integration
The Euler-Type Universal Numerical Integrator (E-TUNI) is a discrete numerical structure that couples a first-order Euler-type numerical integrator with some feed-forward neural network architecture. Thus, E-TUNI can be used to model non-linear dynamic systems when the real-world plant’s analytical...
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| Format: | Article |
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MDPI AG
2025-03-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/18/3/153 |
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| author | Paulo M. Tasinaffo Gildárcio S. Gonçalves Johnny C. Marques Luiz A. V. Dias Adilson M. da Cunha |
| author_facet | Paulo M. Tasinaffo Gildárcio S. Gonçalves Johnny C. Marques Luiz A. V. Dias Adilson M. da Cunha |
| author_sort | Paulo M. Tasinaffo |
| collection | DOAJ |
| description | The Euler-Type Universal Numerical Integrator (E-TUNI) is a discrete numerical structure that couples a first-order Euler-type numerical integrator with some feed-forward neural network architecture. Thus, E-TUNI can be used to model non-linear dynamic systems when the real-world plant’s analytical model is unknown. From the discrete solution provided by E-TUNI, the integration process can be either forward or backward. Thus, in this article, we intend to use E-TUNI in a backward integration framework to model autonomous non-linear dynamic systems. Three case studies, including the dynamics of the non-linear inverted pendulum, were developed to verify the computational and numerical validation of the proposed model. |
| format | Article |
| id | doaj-art-3422bb5ac99f497c902b22a5a29cd4ca |
| institution | DOAJ |
| issn | 1999-4893 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj-art-3422bb5ac99f497c902b22a5a29cd4ca2025-08-20T02:41:45ZengMDPI AGAlgorithms1999-48932025-03-0118315310.3390/a18030153The Euler-Type Universal Numerical Integrator (E-TUNI) with Backward IntegrationPaulo M. Tasinaffo0Gildárcio S. Gonçalves1Johnny C. Marques2Luiz A. V. Dias3Adilson M. da Cunha4Instituto Tecnológico de Aeronáutica (ITA), São José dos Campos 12228-900, SP, BrazilInstituto Tecnológico de Aeronáutica (ITA), São José dos Campos 12228-900, SP, BrazilInstituto Tecnológico de Aeronáutica (ITA), São José dos Campos 12228-900, SP, BrazilInstituto Tecnológico de Aeronáutica (ITA), São José dos Campos 12228-900, SP, BrazilInstituto Tecnológico de Aeronáutica (ITA), São José dos Campos 12228-900, SP, BrazilThe Euler-Type Universal Numerical Integrator (E-TUNI) is a discrete numerical structure that couples a first-order Euler-type numerical integrator with some feed-forward neural network architecture. Thus, E-TUNI can be used to model non-linear dynamic systems when the real-world plant’s analytical model is unknown. From the discrete solution provided by E-TUNI, the integration process can be either forward or backward. Thus, in this article, we intend to use E-TUNI in a backward integration framework to model autonomous non-linear dynamic systems. Three case studies, including the dynamics of the non-linear inverted pendulum, were developed to verify the computational and numerical validation of the proposed model.https://www.mdpi.com/1999-4893/18/3/153Euler-Type Universal Numerical Integratorneural differential equationsnon-linear auto regressive moving average with exogenous inputsRunge–Kutta neural networkuniversal numerical integrator |
| spellingShingle | Paulo M. Tasinaffo Gildárcio S. Gonçalves Johnny C. Marques Luiz A. V. Dias Adilson M. da Cunha The Euler-Type Universal Numerical Integrator (E-TUNI) with Backward Integration Algorithms Euler-Type Universal Numerical Integrator neural differential equations non-linear auto regressive moving average with exogenous inputs Runge–Kutta neural network universal numerical integrator |
| title | The Euler-Type Universal Numerical Integrator (E-TUNI) with Backward Integration |
| title_full | The Euler-Type Universal Numerical Integrator (E-TUNI) with Backward Integration |
| title_fullStr | The Euler-Type Universal Numerical Integrator (E-TUNI) with Backward Integration |
| title_full_unstemmed | The Euler-Type Universal Numerical Integrator (E-TUNI) with Backward Integration |
| title_short | The Euler-Type Universal Numerical Integrator (E-TUNI) with Backward Integration |
| title_sort | euler type universal numerical integrator e tuni with backward integration |
| topic | Euler-Type Universal Numerical Integrator neural differential equations non-linear auto regressive moving average with exogenous inputs Runge–Kutta neural network universal numerical integrator |
| url | https://www.mdpi.com/1999-4893/18/3/153 |
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