N-body Simulations

• Descripton
  Spring: This dataset simulates a system containing 5 particles connected by springs. Particles are located in 2D coordinates without any external forces except elastic collisions. Particles are connected via springs with probability of 0.5, and interactions between springs follow Hooke’s law. The initial location of each particle is sampled from a Gaussian distribution and the initial velocity of each particle is a random vector of norm 0.5. The trajectories of all springs are calculated by solving Newton’s equations of motion PDE. The temporal length of each sequence is 49, which obtains from subsampling every 100 steps in a trajectory.
  Charged: This dataset simulates a system containing 5 particles with positive or negative charges. Particles are located in 2D coordinates without any external forces except attracting force and repelling force. The quantity of electrical charges is sampled from uniform probability. Each particle interacts via Coulomb forces. The initial location of each particle is sampled from a Gaussian distribution and the initial velocity of each particle is a random vector of norm 0.5. The trajectories of all springs are calculated by solving Newton’s equations of motion PDE. The temporal length of each sequence is 49, which obtains from subsampling every 100 steps in a trajectory.
• Statistics:

Name	Type	#Graphs	#Nodes	#Edges	Attributed	Directed	Weighted	Signed	Homogeneous	Spatial	Temporal	Labels
N-body-Spring	Physical Simulation Networks	3,430,000	5	~10	YES	NO	NO	NO	YES	2D	YES	YES
N-body-Charged	Physical Simulation Networks	3,430,000	5	25	YES	NO	NO	NO	YES	2D	YES	YES

• Acknowlegement:
  Kipf, T., Fetaya, E., Wang, K. C., Welling, M., & Zemel, R. (2018, July). Neural relational inference for interacting systems. In International Conference on Machine Learning (pp. 2688-2697). PMLR.