Publications Repository - Helmholtz-Zentrum Dresden-Rossendorf

2 Publications
Solving the Kuramoto Oscillator Model on Random Graphs
Kelling, J.ORC; Ódor, G.ORC; Gemming, G.
The problem of synchronization is recently attracting much attention because it relates to current topics in science. The dynamics of electrical grids can be affected by de-synchronizations between supplier and consumer nodes. In brains, synchronization of neuronal activity plays an important role in most functions. The Kuramoto model describes systems of coupled oscillators which, which exhibit non-trivial behavior on complex graphs, making it a suitable tool to study the synchronization dynamics of brains an other systems.

Numerical solution of Kuramoto type ordinary differential equations for long times and large systems requires strong computation power, due to the inherent chaoticity of this nonlinear system.

This poster presents a GPU implementation of a solver achieving large speedups over CPU on sparse random graphs. The key to performance here, is the presented memory layout which supplements the SIMT usage of our design.

# extended abstract
The problem of synchronization is recently attracting much attention because it relates to current topics in science. The dynamics of electrical grids can be affected by de-synchronizations between supplier and consumer nodes. In brains, synchronization of neuronal activity plays an important role in most functions.

Using the Kuramoto model[1], we are studying a range of problems, from basinc questions about synnchronisation transitions on disordered lattices and random graphs to problems mentioned in the short abstract. The model shows komplex behavior on human connectome graph, which allow the study of synchronization in the human brain[2]. An extension of the model allows modeling power grid networks[3,4].

Very intensive Simulations are required to obtain precise result especiall near criticality, which these systems show at synchronization transitons. To enable the study of these systems at sufficent precision, we implemented a GPU code, which we are presenting in this poster. To this end we used boost::odeint to get the standart numerical integartion out of the way an focus on the most performance critical aspect: the evaluation of the model itself. The key to our implementation is the choice of SIMT vectorization and a suitable memory layout, which are presented in the poster. The aspects also remain the same, when we add the extension to the second-order Kuramoto Model[2], which is required to model powergrids.

[1] Kuramoto, Y. In Araki, H. (ed.) Mathematical Problems in Theoretical Physics, vol. 39 of Lecture Notes in Physics, Berlin, 420
[2] Villegas, P., Moretti, P. & Muñoz, M. A. Scientific Reports 4, 5990 (2014).
[3] Filatrella, G., Nielsen, A. H. & Pedersen, N. F. Eur. Phys. J. B 61, 485–491 (2008)
[4] Ódor, G. & Hartmann, B. Phys. Rev. E 98, 022305 (2018).
Keywords: GPGPU, random graph, Kuramoto model

Publ.-Id: 29004 - Permalink