znicolaou / kuramoto

Integrate a large network of Kuramoto oscillators on a gpu with a random or user-specified adjacency matrix

Integrate a large network of Kuramoto oscillators on a gpu with a random or user-specified adjacency matrix

Files in the kuramoto repository

The files kuramoto.cu and kuramoto_64.cu contains cuda code to numerically integrate phase oscillators on a gpu. They the Dormand-Prince adaptive timestep 4/5 Runge-Kutta integration scheme implemented in dp45.cu and dp45_64.cu. The 64 bit versions use double precision, and the others use single precision.
The jupyter notebook volacno.ibnb plots results.

Installation

Create a conda environment with for the jupyter notebook: conda create -n kuramoto_env numpy scipy jupyter matplotlib. Activate this environment with conda activate kuramoto_env.

The kuramoto.cu program can be compiled on a computer with the nvidia cuda compiler with nvcc -O3 -lcuda -lcublas -lcurand kuramoto.cu dp45.cu -o kuramoto.

Usage

Running ./kuramoto -h produces the following usage message:

usage:	kuramoto [-hvnDRFA] [-N N] [-K K]
	[-c c] [-t t] [-d dt] [-f f] [-s seed] 
	[-I init] [-r rtol] [-a atol] [-g gpu] filebase 

-h for help 
-v for verbose 
-n for normal random frequencies (default is cauchy) 
-D to supress dense output 
-R to reload adjacency, frequencies, and initial conditions from files if possible
-F for fixed timestep 
-A to regenerate volcano adjacency each step to save memory 
N is number of oscillators. Default 5000. 
K is rank of volcano adjacency. Default 5. 
c is the coupling coefficient. Default 3.0. 
t is total integration time. Default 1e2. 
dt is the time between outputs. Default 1e0. 
f is the scale of the frequencies. Default 1e0. 
seed is random seed. Default 1. 
init is uniform random initial condition scale. Default 0. 
rtol is relative error tolerance. Default 0.
atol is absolute error tolerance. Default 1e-6.
gpu is index of the gpu. Default 0.
filebase is base file name for output. 

Output and input files

The kuramoto program requires the positional argument FILEBASE, which is the base name for output and input files.

FILEBASE.out is a text file, which contains the command line that was run on the first line, the runtime, and step information if -v is set.

FILEBASEfs.dat contains the final state of the phases in a binary format. The final time and timestep are appended at the end for restarting simulations with the -R option.

FILEBASEorder.dat contains the order parameter evaluated in steps of dt, in a binary format.

FILEBASEthetas.dat contains the oscillator phases evaluated in steps of dt, in a binary format. If the -D option is set, this output file is not produced.

FILEBASEtimes.dat contains the time steps taken by the integrator, in a binary format. If the -D option is set, this output file is not produced.

FILEBASEadj.dat contains the adjacency matrix in a binary column, major format. If the -D option is set, this output file is not produced. If the -R option is set, the adjacency matrix is loaded from this file rather than being generated randomly.

FILEBASEfrequencies.dat contains the oscillator frequencies in a binary format. If the -R option is set, the frequencies are loaded from this file rather than being generated randomly.