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Dynamical System Algorithms of the Ising Model

发布时间:2021-01-11 作者: 浏览次数:
Speaker: 刘博文 DateTime: 2021年1月12日10:00
Brief Introduction to Speaker:


Place: 腾讯会议腾讯会议(会议号请联系王宇辰老师索取)
Abstract:Various combinatorial optimization NP-hard problems can be reduced to finding the minimizer of an Ising model, which is a discrete mathematical model. Over the past decades, many continuous approaches or algorithms have been proposed from physical, mathematical or computational views for optimizing the Ising model such as quantum annealing, the coherent Ising machine, simulated annealing, adiabatic Hamiltonian systems, etc.. However, the mathematical principle of these algorithms is far from being understood. In this talk, I will introduce the Ising model and review the dynamical system algorithms for the Ising problem. I will talk about our recent results on the mathematical mechanism of dynamical system algorithms by Morse theory and variational methods. Motivated by the works of C. Conley, I will show the transit and capture properties of the simulated bifurcation algorithm to explain its convergence by the low energy transit and capture in celestial mechanics.