Utilizing Tessellation concept in Machine Learning part1
- Efficient Large-Scale Simulation of Fish Schooling Behavior Using Voronoi Tessellations and Fuzzy Clustering(arXiv)
Author : Salah Alrabeei, Talal Rahman, Sam Subbey
Abstract : This paper introduces an efficient approach to reduce the computational cost of simulating collective behaviors, such as fish schooling, using Individual-Based Models (IBMs). The proposed technique employs adaptive and dynamic load-balancing domain partitioning, which utilizes unsupervised machine-learning models to cluster a large number of simulated individuals into sub-schools based on their spatial-temporal locations. It also utilizes Voronoi tessellations to construct non-overlapping simulation subdomains. This approach minimizes agent-to-agent communication and balances the load both spatially and temporally, ultimately resulting in reduced computational complexity. Experimental simulations demonstrate that this partitioning approach outperforms the standard regular grid-based domain decomposition, achieving a reduction in computational cost while maintaining spatial and temporal load balance. The approach presented in this paper has the potential to be applied to other collective behavior simulations requiring large-scale simulations with a substantial number of individuals
2. Effective electrical conductivity of random resistor networks generated using a Poisson — Voronoi tessellation(arXiv)
Author : Yuri Yu. Tarasevich, Irina V. Vodolazskaya, Andrei V. Eserkepov
Abstract : We studied the effective electrical conductivity of dense random resistor networks (RRNs) produced using a Voronoi tessellation when its seeds are generated by means of a homogeneous Poisson point process in the two-dimensional Euclidean space. Such RRNs are isotropic and in average homogeneous, however, local fluctuations of the number of edges per unit area are inevitably. These RRNs may mimic, e.g., crack-template-based transparent conductive films. The RRNs were treated within a mean-field approach (MFA). We found an analytical dependency of the effective electrical conductivity on the number of conductive edges (resistors) per unit area, nE. The effective electrical conductivity is proportional to nE−−√ when nE≫1.
