An Orthogonal Polynomial Kernel-Based Machine Learning Model for Differential-Algebraic Equations
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913209520226304 |
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| author | Taheri, Tayebeh Aghaei, Alireza Afzal Parand, Kourosh |
| author_facet | Taheri, Tayebeh Aghaei, Alireza Afzal Parand, Kourosh |
| contents | The recent introduction of the Least-Squares Support Vector Regression (LS-SVR) algorithm for solving differential and integral equations has sparked interest. In this study, we expand the application of this algorithm to address systems of differential-algebraic equations (DAEs). Our work presents a novel approach to solving general DAEs in an operator format by establishing connections between the LS-SVR machine learning model, weighted residual methods, and Legendre orthogonal polynomials. To assess the effectiveness of our proposed method, we conduct simulations involving various DAE scenarios, such as nonlinear systems, fractional-order derivatives, integro-differential, and partial DAEs. Finally, we carry out comparisons between our proposed method and currently established state-of-the-art approaches, demonstrating its reliability and effectiveness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14382 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Orthogonal Polynomial Kernel-Based Machine Learning Model for Differential-Algebraic Equations Taheri, Tayebeh Aghaei, Alireza Afzal Parand, Kourosh Numerical Analysis Machine Learning The recent introduction of the Least-Squares Support Vector Regression (LS-SVR) algorithm for solving differential and integral equations has sparked interest. In this study, we expand the application of this algorithm to address systems of differential-algebraic equations (DAEs). Our work presents a novel approach to solving general DAEs in an operator format by establishing connections between the LS-SVR machine learning model, weighted residual methods, and Legendre orthogonal polynomials. To assess the effectiveness of our proposed method, we conduct simulations involving various DAE scenarios, such as nonlinear systems, fractional-order derivatives, integro-differential, and partial DAEs. Finally, we carry out comparisons between our proposed method and currently established state-of-the-art approaches, demonstrating its reliability and effectiveness. |
| title | An Orthogonal Polynomial Kernel-Based Machine Learning Model for Differential-Algebraic Equations |
| topic | Numerical Analysis Machine Learning |
| url | https://arxiv.org/abs/2401.14382 |