Machine-learning Closure for Vlasov-Poisson Dynamics in Fourier-Hermite Space
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915560740093952 |
|---|---|
| author | Barbour, Nathaniel Dorland, William Abel, Ian G. Landreman, Matt |
| author_facet | Barbour, Nathaniel Dorland, William Abel, Ian G. Landreman, Matt |
| contents | Accurate reduced models of turbulence are desirable to facilitate the optimization of magnetic-confinement fusion reactor designs. As a first step toward higher-dimensional turbulence applications, we use reservoir computing, a machine-learning (ML) architecture, to develop a closure model for a limiting case of electrostatic gyrokinetics. We implement a pseudo-spectral Eulerian code to solve the one-dimensional Vlasov-Poisson system on a basis of Fourier modes in configuration space and Hermite polynomials in velocity space. When cast onto the Hermite basis, the Vlasov equation becomes an infinitely coupled hierarchy of fluid moments, presenting a closure problem. We exploit the locality of interactions in the Hermite representation to introduce an ML closure model of the small-scale dynamics in velocity space. In the linear limit, when the kinetic Fourier-Hermite solver is augmented with the reservoir closure, the closure permits a reduction of the velocity resolution, with a relative error within two percent for the Hermite moment where the reservoir closes the hierarchy. In the strongly-nonlinear regime, the ML closure model more accurately resolves the low-order Fourier and Hermite spectra when compared to a naïve closure by truncation and reduces the required velocity resolution by a factor of sixteen. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13313 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Machine-learning Closure for Vlasov-Poisson Dynamics in Fourier-Hermite Space Barbour, Nathaniel Dorland, William Abel, Ian G. Landreman, Matt Plasma Physics Accurate reduced models of turbulence are desirable to facilitate the optimization of magnetic-confinement fusion reactor designs. As a first step toward higher-dimensional turbulence applications, we use reservoir computing, a machine-learning (ML) architecture, to develop a closure model for a limiting case of electrostatic gyrokinetics. We implement a pseudo-spectral Eulerian code to solve the one-dimensional Vlasov-Poisson system on a basis of Fourier modes in configuration space and Hermite polynomials in velocity space. When cast onto the Hermite basis, the Vlasov equation becomes an infinitely coupled hierarchy of fluid moments, presenting a closure problem. We exploit the locality of interactions in the Hermite representation to introduce an ML closure model of the small-scale dynamics in velocity space. In the linear limit, when the kinetic Fourier-Hermite solver is augmented with the reservoir closure, the closure permits a reduction of the velocity resolution, with a relative error within two percent for the Hermite moment where the reservoir closes the hierarchy. In the strongly-nonlinear regime, the ML closure model more accurately resolves the low-order Fourier and Hermite spectra when compared to a naïve closure by truncation and reduces the required velocity resolution by a factor of sixteen. |
| title | Machine-learning Closure for Vlasov-Poisson Dynamics in Fourier-Hermite Space |
| topic | Plasma Physics |
| url | https://arxiv.org/abs/2504.13313 |