Point convolutional neural network algorithm for Ising model ground state research based on spring vibration

Abstract

The ground state search of the Ising model can be used to solve many combinatorial optimization problems. Under the current computer architecture, an Ising ground state search algorithm suitable for hardware computing is necessary for solving practical problems. Inspired by the potential energy conversion of the springs, we propose the Spring-Ising Algorithm, a point convolutional neural network algorithm for ground state search based on the spring vibration model. Spring-Ising Algorithm regards the spin as a moving mass point connected to a spring and establishes the equation of motion for all spins. Spring-Ising Algorithm can be mapped on AI chips through the basic structure of the neural network for fast and efficient parallel computing. The algorithm has shown promising results in solving the Ising model and has been tested in the recognized test benchmark K2000. The optimal results of this algorithm after 10,000 steps of iteration are 2.9% of all results. The algorithm introduces the concept of dynamic equilibrium to achieve a more detailed local search by dynamically adjusting the weight of the Ising model in the spring oscillation model. Spring-Ising Algorithm offers the possibility to calculate the Ising model on a chip which focuses on accelerating neural network calculations.