Learning phase-space flows using time-discrete implicit Runge-Kutta PINNs
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910619500806144 |
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| author | Corral, Álvaro Fernández Mendoza, Nicolás Iske, Armin Yachmenev, Andrey Küpper, Jochen |
| author_facet | Corral, Álvaro Fernández Mendoza, Nicolás Iske, Armin Yachmenev, Andrey Küpper, Jochen |
| contents | We present a computational framework for obtaining multidimensional phase-space solutions of systems of non-linear coupled differential equations, using high-order implicit Runge-Kutta Physics- Informed Neural Networks (IRK-PINNs) schemes. Building upon foundational work originally solving differential equations for fields depending on coordinates [J. Comput. Phys. 378, 686 (2019)], we adapt the scheme to a context where the coordinates are treated as functions. This modification enables us to efficiently solve equations of motion for a particle in an external field. Our scheme is particularly useful for explicitly time-independent and periodic fields. We apply this approach to successfully solve the equations of motion for a mass particle placed in a central force field and a charged particle in a periodic electric field. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_16826 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning phase-space flows using time-discrete implicit Runge-Kutta PINNs Corral, Álvaro Fernández Mendoza, Nicolás Iske, Armin Yachmenev, Andrey Küpper, Jochen Machine Learning Artificial Intelligence Numerical Analysis Dynamical Systems We present a computational framework for obtaining multidimensional phase-space solutions of systems of non-linear coupled differential equations, using high-order implicit Runge-Kutta Physics- Informed Neural Networks (IRK-PINNs) schemes. Building upon foundational work originally solving differential equations for fields depending on coordinates [J. Comput. Phys. 378, 686 (2019)], we adapt the scheme to a context where the coordinates are treated as functions. This modification enables us to efficiently solve equations of motion for a particle in an external field. Our scheme is particularly useful for explicitly time-independent and periodic fields. We apply this approach to successfully solve the equations of motion for a mass particle placed in a central force field and a charged particle in a periodic electric field. |
| title | Learning phase-space flows using time-discrete implicit Runge-Kutta PINNs |
| topic | Machine Learning Artificial Intelligence Numerical Analysis Dynamical Systems |
| url | https://arxiv.org/abs/2409.16826 |