Particle Control in Phase Space by Global K-Means Clustering

TY - JOUR

T1 - Particle Control in Phase Space by Global K-Means Clustering

AU - Frederiksen, Jacob Trier

AU - Lapenta, G.

AU - Pessah, M. E.

N1 - 14 pages, 19 figures, in preparation

PY - 2015/11/30

Y1 - 2015/11/30

N2 - We devise and explore an iterative optimization procedure for controlling particle populations in particle-in-cell (PIC) codes via merging and splitting of computational macro-particles. Our approach, is to compute an optimal representation of the global particle phase space structure while decreasing or increasing the entire particle population, based on k-means clustering of the data. In essence the procedure amounts to merging or splitting particles by statistical means, throughout the entire simulation volume in question, while minimizing a 6-dimensional total distance measure to preserve the physics. Particle merging is by far the most demanding procedure when considering conservation laws of physics; it amounts to lossy compression of particle phase space data. We demonstrate that our k-means approach conserves energy and momentum to high accuracy, even for high compression ratios, R≈3 --- \emph{i.e.}, Nf≲0.33Ni. Interestingly, we find that an accurate particle splitting step can be performed using k-means as well; this from an argument of symmetry. The split solution, using k-means, places splitted particles optimally, to obtain maximal spanning on the phase space manifold. Implementation and testing is done using an electromagnetic PIC code, the Photon-Plasma code. Nonetheless, the k-means framework is general; it is not limited to Vlasov-Maxwell type PIC codes. We discuss advantages and drawbacks of this optimal phase space reconstruction.

AB - We devise and explore an iterative optimization procedure for controlling particle populations in particle-in-cell (PIC) codes via merging and splitting of computational macro-particles. Our approach, is to compute an optimal representation of the global particle phase space structure while decreasing or increasing the entire particle population, based on k-means clustering of the data. In essence the procedure amounts to merging or splitting particles by statistical means, throughout the entire simulation volume in question, while minimizing a 6-dimensional total distance measure to preserve the physics. Particle merging is by far the most demanding procedure when considering conservation laws of physics; it amounts to lossy compression of particle phase space data. We demonstrate that our k-means approach conserves energy and momentum to high accuracy, even for high compression ratios, R≈3 --- \emph{i.e.}, Nf≲0.33Ni. Interestingly, we find that an accurate particle splitting step can be performed using k-means as well; this from an argument of symmetry. The split solution, using k-means, places splitted particles optimally, to obtain maximal spanning on the phase space manifold. Implementation and testing is done using an electromagnetic PIC code, the Photon-Plasma code. Nonetheless, the k-means framework is general; it is not limited to Vlasov-Maxwell type PIC codes. We discuss advantages and drawbacks of this optimal phase space reconstruction.

KW - astro-ph.IM

KW - astro-ph.HE

KW - physics.comp-ph

KW - physics.plasm-ph

M3 - Journal article

SN - 0021-9991

JO - Journal of Computational Physics

JF - Journal of Computational Physics

ER -