Machine-learning Closure for Vlasov-Poisson Dynamics in Fourier-Hermite Space
arXiv:2504.13313 · doi:10.1017/S0022377825100822
Abstract
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.
Updated version that was accepted for publication in Journal of Plasma Physics. Includes a new section, appendix, and four new figures. 24 pages, 15 figures, 1 table in total
References in corpus (28)
- SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
- Array Programming with NumPy
- Data-driven prediction of a multi-scale Lorenz 96 chaotic system using deep learning methods: Reservoir computing, ANN, and RNN-LSTM
- Reduced fluid-kinetic equations for low-frequency dynamics, magnetic reconnection and electron heating in low-beta plasmas
- Critically balanced ion temperature gradient turbulence in fusion plasmas
- Fast collisionless reconnection and electron heating in strongly magnetized plasmas
- Fluidization of collisionless plasma turbulence
- Two-dimensional gyrokinetic turbulence
- Laguerre-Hermite Pseudo-Spectral Velocity Formulation of Gyrokinetics
- Free energy cascade in gyrokinetic turbulence
- Fourier-Hermite spectral representation for the Vlasov-Poisson system in the weakly collisional limit
- Viriato: a Fourier-Hermite spectral code for strongly magnetised fluid-kinetic plasma dynamics
- Fluctuation-dissipation relations for a plasma-kinetic Langevin equation
- Machine Learning Surrogate Models for Landau Fluid Closure
- A solvable model of Vlasov-kinetic plasma turbulence in Fourier-Hermite phase space
- A Drift-Kinetic Analytical Model for SOL Plasma Dynamics at Arbitrary Collisionality
- Applications of Large Eddy Simulation methods to gyrokinetic turbulence
- Optimisation of confinement in a fusion reactor using a nonlinear turbulence model
- Critical gradient turbulence optimization toward a compact stellarator reactor concept
- Data-driven, multi-moment fluid modeling of Landau damping
- Data-driven modeling of Landau damping by physics-informed neural networks
- Gyrokinetic turbulence: between idealized estimates and a detailed analysis of nonlinear energy transfers
- Machine-learning heat flux closure for multi-moment fluid modeling of nonlinear Landau damping
- In Search of a Data Driven Symbolic Multi-Fluid 10-Moment Model Closure
- Gyrokinetic simulations of plasma turbulence in a Z-pinch using a moment based approach and advanced collision operators
- Full-F Turbulent Simulation in a Linear Device using a Gyro-Moment Approach
- Data-driven discovery of a heat flux closure for electrostatic plasma phenomena
- An analytical form of the dispersion function for local linear gyrokinetics in a curved magnetic field